A couple of changes to Dundee's starting line-up. Ryan Astley and Fin Robertson came in for the suspended Lyall Cameron and for Mo Sylla, who was on the bench.
Dundee started well enough and forced a couple of corners which were well defended by the home team. The only chance for Hearts when a quick break away Vargas put his shot wide of the post.
The opening 25 minutes were both teams testing each other out without any clear cut chances. But on 27 minutes Hearts scored when a quick throw in was knocked on to Kartum to curl the ball past Carson who had no chance of saving.
This changed the games flow a bit. Dundee hit on the break but failed to test Gordon in the Hearts goal. Hearts had a goal disallowed for offside.
As half-time drew close Dundee had a great chance a quick break and the ball was knocked forward to Adewumi who was clear, but his shot smashed of the frame of the goal. It was so close to being a goal.
Second half and Mo Sylla came on to replace Jordan McGhee in midfield at half time.
Hearts had a couple of attacks and Dundee managed to clear the ball.
But the next period it was all Dundee as they attacked with pace. Then on 50 minutes when a quick throw in was played Ziyad Larkeche dug out a superb cross from the byline. Joe Shaughnessy had stayed up after the previous corner and headed neatly across Gordon to bring the Dark Blues back onto level terms.
The next 10 minutes it was all Dundee and they came close twice with good efforts on goal, another couple of attacks failed as maybr feeding Adewumi in as he had space.
Then Dundee had a narrow escape when Hearts broke across the halfway line. Sylla fouled Vargas, but referee Kevin Clancy played the advantage allowing Kabangu to run clear. Cesar Garza sprinted back to put in a superb challenge as Kabunga shot.
From the corner Murray headed the ball clear on the line. But the game had swung back for Hearts, they then got a soft free-kick as it was put in and the ball hit the top of Murray's head and ball ended up in the net leaving Carson helpless.
Worse was to follow 5 minutes later, good turn and finish from Kartum put the score to 3-1 and put the game beyond Dundee. Hearts could have scored more but Trevor Carson made three great saves.
Dundee kept at it but the ball would not fall right in the box, they did score but it was offside. Hearts finished the game comfy enough as the third goal sealed the win.
Dundee tried second half as they were much better in the second half. Now they must focus on the league games left this season.
Dundee: Carson, Astley, Shaughnessy (c), Donnelly, Mulligan, Garza (Reilly 82), McGhee (Sylla at half time), Fin Robertson, Larkeche (Tiffoney 74), Adewumi, Murray. Unused Subs: McCracken (gk), Sharp (gk), Ingram, Samuels, Lopez.
Referee: Kevin Clancy.
Att: 17,975.