Alan Forrest (right) doubled Hearts' lead
Hearts further dented Dundee's fading European hopes with a solid Scottish Premiership win in the sunshine at Tynecastle.
Kenneth Vargas volleyed Hearts in front in the first half, Alan Forrest evaded goalkeeper Jon McCracken for their second after the break and Lawrence Shankland added a late third.
Dundee, who trail fifth-placed St Mirren by five points with two games to go, threatened through Luke McCowan and Ryan Howley.
And Tony Docherty's side will lament a missed opportunity, with St Mirren remaining on course for the final European qualifying place despite having lost at home to Kilmarnock.
Hearts, having already clinched third, can breach the 70-point mark by winning their final two games.
Ryan Astley's intervention prevented Forrest connecting with Vargas' cut-back as Hearts tried to find an early breakthrough.
McCracken was called into action to deal with a deflected Forrest shot and the Dundee goalkeeper excelled by palming away a Vargas header moments later.
Dundee had a sight of goal as Astley headed over at a corner and Hearts quickly went up the other end and scored.
Barrie McKay teased the Dundee defence in the inside left area and lifted a cross to the back post for Vargas to finish. VAR confirmed Vargas was onside.
The visitors thought they had a penalty when referee Nick Walsh pointed to the spot after Lyall Cameron's shot deflected off Stephen Kingsley.
Upon review, Walsh overturned his handball decision and signalled for a Dundee corner.
McKay was also instrumental to Hearts' second, his piercing through ball allowing Forrest to beat the offside trap, round McCracken and roll the ball over the line.
Youngster James Wilson tested McCracken at his near left post as Hearts threatened to run away with it.
Dundee needed a response but Craig Gordon's clean sheet remained intact with Dundee captain McCowan's low strike and Michael Mellon's effort kept out by the veteran goalkeeper either side of Howley firing just wide.
And Shankland added gloss to the scoreline as the game ticked in to added time. Despite having a relatively quiet game, the league's top scorer peeled off the Dundee defence expertly to receive substitute Scott Fraser's pass and apply the finish - goal number 25 of the season.
Player of the match - Barrie McKay (Hearts)
It's been an injury interrupted season for the Hearts winger (left) but he showed what he has to offer with two assists
Hearts' strong campaign continues - analysis
With this, a 20th win from 36 in the league so far, Hearts showed once again why they are the envy of similarly-resourced Aberdeen and city rivals Hibernian.
Options such as Forrest, McKay and Vargas, in addition to top scorer and PFA Scotland player of the year Shankland, mean Steven Naismith's side will always create chances but their defensive prowess is just as impressive.
Only Celtic and Rangers have conceded fewer goals this term.
Dundee sustain a third top-six defeat out of three and are in danger of seeing their impressive season fizzle out.
Still, the Dens Park side still have lots to boast about after a top-half finish on their return to the Premiership.
What the managers said
Hearts head coach Steven Naismith reacts to win over Dundee
Hearts head coach Steven Naismith: "Good performance, clean sheet first of all. We were secure out of possession. When we started moving the ball quicker in the second half, we created more chances and we scored some good goals so, yeah, pleasing afternoon.
"[Barrie McKay's] quality is there. He's still not fit so that's a work in progress. He's got unbelievable quality. We rotated the team and we will do the rest of the week. We trust every player that plays."
Dundee manager Tony Docherty: "I don't think it was ever a 3-0. I was really pleased with the level of performance I got from the players. Not pleased with the goals we conceded, particularly the first two. We did create numerous opportunities.
"If you're at Dundee, you don't get VAR decisions. It's been a whole season of it. I think it's a penalty. There's contact and the ball's going towards the goal. It's so harsh on us."
Dundee manager Tony Docherty reacts to defeat by Hearts
What's next?
Dundee visit Rangers on Tuesday (19:30 BST), with Hearts away to St Mirren the following night (19:45).
