A sickener for Livingston after two goals from Stephen Kelly had them in front.
But Hearts woke up and smashed in four goals in 22 minutes to make it 4-2 before half-time.
Jorge Grant started it, then Yutaro Oda and Cammy Devlin scored similar goals by tapping in crosses from close-range.
Then Lawrence Shankland added a penalty when Oda was felled by Shamal George.
Hearts stay 11 points clear in third spot. Livingston are circling the drain, as they remain nine adrift at the bottom with five games left.
SNSCopyright: SNS
Lawrence Shankland crashes in a penalty for HeartsImage caption: Lawrence Shankland crashes in a penalty for Hearts
RED CARD
Aberdeen 0-0 Dundee
Graeme Shinnie - that is very, very naughty.
Already on a yellow, he goes studs up on Malachi Boateng, nowhere near the ball. It's poor from the Dons skipper.
FULL-TIME St Johnstone 0-2 Kilmarnock
A massive win for Kilmarnock, who move eight points clear of St Mirren in fourth-place.
Joe Wright and Marley Watkins grabbed the all-important goals to secure their side's third away league win of the season.
After a poor first half, St Johnstone improved but failed to find the net. They remain 10th in the Premiership.
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FULL-TIME Celtic 3-0 St Mirren
Celtic move four points clear at the top of the Premiership after coming to life in the second half to overcome stubborn St Mirren.
After failing to muster an effort on target before the break, the reigning champions settled the game with two sublime finishes from Japan duo Reo Hatate and Kyogo Furuhashi within 15 minutes of the restart.
Adam Idah's close-range header in the closing stages was the icing on the cake.
SNSCopyright: SNS
Kyogo Furuhashi's 16th goal of the season put Celtic 2-0 aheadImage caption: Kyogo Furuhashi's 16th goal of the season put Celtic 2-0 ahead
Post update
Aberdeen 0-0 Dundee
Dundee have suddenly parked the bus and invited pressure - and Stefan Gartenmann has just put a bicycle kick inches over the bar!
It's not done yet...
Post update
Aberdeen 0-0 Dundee
We're three minutes into eight minutes of stoppage time.
Dundee just need to shut up shop for a first top six finish since 2015.
CLOSE!
St Johnstone 0-2 Kilmarnock
Oh my. St Johnstone substitute Benjamin Mbunga Kimpioka almost nets a goal of the season contender.
His bicycle kick flies just over the bar. Could've been an all-time beauty there...
FULL-TIME Motherwell 1-1 Hibernian
Motherwell are out of the race of top six.
Hibs need a late favour from Aberdeen to stay alive...
An incredible goal from Shane Blaney levelled for the hosts deep into stoppage time.
SNSCopyright: SNS
CLOSE!
Motherwell 1-1 Hibernian
Oh my word, Oli Shaw should win it for Motherwell but somehow stabs wide from a yard or so!
GOAL Motherwell 1-1 Hibernian
Shane Blaney
A rocket of a finish from Shane Blaney!
The ball drops over the defender's shoulder and he has a swing, catching it so cleanly.
It whizzes past David Marshall in a blur.
BBCCopyright: BBC
GOAL Ayr United 5-0 Arbroath
Logan Chalmers
GOAL Celtic 3-0 St Mirren
Adam Idah
Free and easy for Celtic now.
Adam Idah's heads home from close range after goalkeeper Zach Hemming blocked Matt O'Riley's low drive.
BBCCopyright: BBC
Post update
Aberdeen 0-0 Dundee
Dundee are putting Aberdeen under real pressure. In the latest scramble in the box there are two attempted overhead kicks, but the best effort comes from Aaron Donnelly, slashing the ball at goal - but it's blocked.
GREAT SAVE!
Celtic 2-0 St Mirren
So nearly a third for Celtic, but goalkeeper Zach Hemming does superbly to turn over a fine drive from substitute winger Luis Palma.
GOAL St Johnstone 0-2 Kilmarnock
Marley Watkins
Is that all three points heading back to Ayrshire?
Marley Watkins stabs in at the back post after St Johnstone fail to defend a deep free-kick delivery from Daniel Armstrong.
BBCCopyright: BBC
Post update
Aberdeen 0-0 Dundee
Curtis Main is just on and he's handed a golden opportunity by Lyall Cameron, who slides him through on goal.
But the Dundee striker takes an atrocious touch that slows him right down and a defender catches up to block the shot. The Aberdeen fans don't look too surprised...
GREAT SAVE!
St Johnstone 0-1 Kilmarnock
Will Dennis keeps Kilmarnock ahead with a fine stop.
Ryan McGowan pounces on a loose ball at the back post, but his prodded effort is excellently tipped onto the post by the Killie number one and eventually cleared to safety.
Post update
Motherwell 0-1 Hibernian
That penalty from Myziane Maolida makes it advantage to Hibs in the top six race.
Motherwell need a two-goal turnaround to have a chance.
A goal for Dundee at Pittodrie would change the picture completely.
SNSCopyright: SNS
Post update
Motherwell 0-1 Hibernian
Elie Youan does really well to race into the Hibs' final third to lay it off for Myziane Maolida whose run is cut out by a claret and amber shirt and Motherwell have a goal-kick.
Up the other end, Moses Ebiye has a chance in the middle of the box but he scuffs his attempted volley and it trickles out of play.
Post update
St Johnstone 0-1 Kilmarnock
How are Kilmarnock not further ahead?
This time Dimitar Mitov keeps out a strong header from Liam Donnelly before the hosts desperately hack the ball clear.
Live Reporting
Colin Moffat
All times stated are UK
FULL-TIME - Hearts 4-2 Livingston
A sickener for Livingston after two goals from Stephen Kelly had them in front.
But Hearts woke up and smashed in four goals in 22 minutes to make it 4-2 before half-time.
Jorge Grant started it, then Yutaro Oda and Cammy Devlin scored similar goals by tapping in crosses from close-range.
Then Lawrence Shankland added a penalty when Oda was felled by Shamal George.
Hearts stay 11 points clear in third spot. Livingston are circling the drain, as they remain nine adrift at the bottom with five games left.
RED CARD
Aberdeen 0-0 Dundee
Graeme Shinnie - that is very, very naughty.
Already on a yellow, he goes studs up on Malachi Boateng, nowhere near the ball. It's poor from the Dons skipper.
FULL-TIME St Johnstone 0-2 Kilmarnock
A massive win for Kilmarnock, who move eight points clear of St Mirren in fourth-place.
Joe Wright and Marley Watkins grabbed the all-important goals to secure their side's third away league win of the season.
After a poor first half, St Johnstone improved but failed to find the net. They remain 10th in the Premiership.
FULL-TIME Celtic 3-0 St Mirren
Celtic move four points clear at the top of the Premiership after coming to life in the second half to overcome stubborn St Mirren.
After failing to muster an effort on target before the break, the reigning champions settled the game with two sublime finishes from Japan duo Reo Hatate and Kyogo Furuhashi within 15 minutes of the restart.
Adam Idah's close-range header in the closing stages was the icing on the cake.
Post update
Aberdeen 0-0 Dundee
Dundee have suddenly parked the bus and invited pressure - and Stefan Gartenmann has just put a bicycle kick inches over the bar!
It's not done yet...
Post update
Aberdeen 0-0 Dundee
We're three minutes into eight minutes of stoppage time.
Dundee just need to shut up shop for a first top six finish since 2015.
CLOSE!
St Johnstone 0-2 Kilmarnock
Oh my. St Johnstone substitute Benjamin Mbunga Kimpioka almost nets a goal of the season contender.
His bicycle kick flies just over the bar. Could've been an all-time beauty there...
FULL-TIME Motherwell 1-1 Hibernian
Motherwell are out of the race of top six.
Hibs need a late favour from Aberdeen to stay alive...
An incredible goal from Shane Blaney levelled for the hosts deep into stoppage time.
CLOSE!
Motherwell 1-1 Hibernian
Oh my word, Oli Shaw should win it for Motherwell but somehow stabs wide from a yard or so!
GOAL Motherwell 1-1 Hibernian
Shane Blaney
A rocket of a finish from Shane Blaney!
The ball drops over the defender's shoulder and he has a swing, catching it so cleanly.
It whizzes past David Marshall in a blur.
GOAL Ayr United 5-0 Arbroath
Logan Chalmers
GOAL Celtic 3-0 St Mirren
Adam Idah
Free and easy for Celtic now.
Adam Idah's heads home from close range after goalkeeper Zach Hemming blocked Matt O'Riley's low drive.
Post update
Aberdeen 0-0 Dundee
Dundee are putting Aberdeen under real pressure. In the latest scramble in the box there are two attempted overhead kicks, but the best effort comes from Aaron Donnelly, slashing the ball at goal - but it's blocked.
GREAT SAVE!
Celtic 2-0 St Mirren
So nearly a third for Celtic, but goalkeeper Zach Hemming does superbly to turn over a fine drive from substitute winger Luis Palma.
GOAL St Johnstone 0-2 Kilmarnock
Marley Watkins
Is that all three points heading back to Ayrshire?
Marley Watkins stabs in at the back post after St Johnstone fail to defend a deep free-kick delivery from Daniel Armstrong.
Post update
Aberdeen 0-0 Dundee
Curtis Main is just on and he's handed a golden opportunity by Lyall Cameron, who slides him through on goal.
But the Dundee striker takes an atrocious touch that slows him right down and a defender catches up to block the shot. The Aberdeen fans don't look too surprised...
GREAT SAVE!
St Johnstone 0-1 Kilmarnock
Will Dennis keeps Kilmarnock ahead with a fine stop.
Ryan McGowan pounces on a loose ball at the back post, but his prodded effort is excellently tipped onto the post by the Killie number one and eventually cleared to safety.
Post update
Motherwell 0-1 Hibernian
That penalty from Myziane Maolida makes it advantage to Hibs in the top six race.
Motherwell need a two-goal turnaround to have a chance.
A goal for Dundee at Pittodrie would change the picture completely.
Post update
Motherwell 0-1 Hibernian
Elie Youan does really well to race into the Hibs' final third to lay it off for Myziane Maolida whose run is cut out by a claret and amber shirt and Motherwell have a goal-kick.
Up the other end, Moses Ebiye has a chance in the middle of the box but he scuffs his attempted volley and it trickles out of play.
Post update
St Johnstone 0-1 Kilmarnock
How are Kilmarnock not further ahead?
This time Dimitar Mitov keeps out a strong header from Liam Donnelly before the hosts desperately hack the ball clear.