Stuart Findlay's diving header won the game in stoppage time for Hearts
Two second-half goals from centre-back Stuart Findlay - including the winner in the 94th minute - stunned Dundee United as Hearts salvaged their 100% start to the Scottish Premiership campaign.
A pulsating game in the Tannadice sunshine deserved a dramatic ending, and Findlay delivered it as he stooped in stoppage time to head in Alexandros Kyziridis' corner.
It was the defender's fourth goal of this nascent season, having bulleted his third into the top corner to draw Hearts level at 2-2 after the break.
The outcome was heartbreaking for a depleted Dundee United side who had themselves come back from a goal down to lead.
Lawrence Shankland's penalty after Findlay was bundled over by Iurie Iovu broke the deadlock, before Ivan Dolcek took centre stage for United.
The Croatian curled in a free-kick just three minutes after Shankland's opener, and then fired in a second at the near post before half-time.
Hearts goalkeeper Zander Clark got a hand to both efforts and was livid he could keep neither out.
But fortunately for him, Findlay bailed him out with two expertly-taken goals from corners.
It means Hearts have won both of their league games so far, as well as four League Cup victories at the start of the season, to give Derek McInnes the perfect start at Tynecastle.
United have European football to focus on come Thursday, but for all of their efforts here they have just the point they gained at Falkirk last week.
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What was the main talking point?
If it was not for Findlay's heroics, Clark's errors for both of United's goals would have been the main talking point, particularly given Scotland's lack of goalkeeping options.
The fact the 33-year-old raced straight to Findlay after the game to embrace him, suggested he knew it, too.
But the plaudits have to go to the former Kilmarnock defender, who was such a pivotal player for McInnes at Rugby Park.
His mere presence in the box caused havoc, first by enticing Iovu to haul him to the ground for the penalty, and then for his tremendous headers.
The first was a bullet into the top corner after Milne's ferocious outswinging corner, and the second was a deft flick back across himself as his face approached the turf.
Which players stood out?
Other than the totemic Findlay for Hearts, Milne and Braga were the standout players.
The former for his brilliant deliveries and energy from left wing-back, the latter for his little moments of quality in the final third.
United had their fair shair of standout performances. Dolcek, who struggled in his first couple of appearances, now has three United goals and possesses undoubted skill.
Midfielder Panutche Camara was replaced on 65 minutes after putting in another exemplary shift. He won the ball back six times, more than any other player.
As well as that, his brilliant pass slid in Dolcek for United's second goal.
The standout stats
That's four goals for the season now for Findlay, as many goals as he has scored in the previous five years and five months.
Dolcek's efforts had an expected goals rating of 0.134 and 0.042, which tells you the goalkeeper should have done better despite both being decent strikes
The Croatian is the first player to score in his first two top-flight games for Dundee United since Opta started collecting data in 2005
Harry Milne created four chances, more than any Hearts player
Panutche Camara has two assists in his first two Premiership games
What did they say?
Dundee United manager Jim Goodwin: "It's never a good time to concede a goal, but it's disappointing the fashion we did. The three goals we conceded here today, a penalty which is avoidable. A defender goes to ground needlessly in my opinion and gives the referee a decision to make.
"[Stuart] Findlay gets himself free of his marker on two occasions, and that's what cost us the game today."
Hearts head coach Derek McInnes: "Every victory is different and a late winner is magnificent. It says a lot about the squad, the spirit and perseverance. You want to get the reputation if we can for being the best team in the league at set plays. They were a huge part today.
What's next for these teams?
Hearts are away to St Mirren next Saturday in the last 16 of the Premier Sports Cup (15:00 BST).
Dundee United host Kilmarnock on Sunday (15:00) in the same competition, but before that they face the return leg of their Conference League qualifier against Rapid Vienna on Thursday (19:45) after a 2-2 first-leg draw.
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