Steven Naismith's side are running away from the chasing pack in third after a superb run of results both before and after the winter break.
Match preview
Hearts continued their charge for a spot in the Europa League last weekend by beating Aberdeen 2-0 at Tynecastle, which extended their unbeaten run to eight games, where they have won seven, and many have come late on in proceedings.
A stunning 2-0 win at Celtic kick-started this run, and a stoppage-time winner from Lawrence Shankland saw them beat rivals Hibernian in the Edinburgh derby.
More late shows have followed, including in the reverse fixture which was played just over a week ago after an initial postponement, as Hearts came from 2-0 down to beat Dundee 3-2, with Yutaro Oda scoring the 86th-minute winner.
Over the past seven games in the Premiership, Hearts have more points than any other side, as their tally of 19 is better than both Rangers (18) and Celtic (15).
That has resulted in a huge gulf opening up between Hearts and the rest of the sides below them, as there is now a 10-point buffer to themselves and Kilmarnock in fourth.
Despite not impressing greatly since the return of league action, Dundee now join Hearts in the top six, which provides a place in the Championship Group when the league splits after 33 games.
Tony Docherty's men have only taken four points from a possible nine since the resumption of the Premiership, but that has been enough to move them up two places to sixth.
A 4-1 victory against bottom-of-the-table Livingston remains their only win in six, but Dundee have taken advantage of other sides around them being out of form entirely.
It was their 1-1 draw at Aberdeen which brought Barry Robson's tenure at Pittodrie to an end and means they enter the weekend above Hibs on goal difference.
While clubs behind them are breathing down their neck for a spot in the top six, Dundee will have eyes on Kilmarnock and St Mirren above them, considering they have two games in hand, and a deficit that is surmountable.
Dundee Scottish Premiership form:
W
L
D
L
W
D
Dundee form (all competitions):
L
D
L
L
W
D
Hearts Scottish Premiership form:
W
W
D
W
W
W
Hearts form (all competitions):
W
D
W
W
W
W
Team News
Dundee will be able to welcome back Luke McCowan from suspension after he sat out the draw at Aberdeen in midweek, but Juan Portales remains out with a hamstring injury.
The hosts have been active in the market, re-signing Owen Beck from Liverpool after he spent the first half of the season at Dens Park.
Michael Mellon and Owen Dodgson have also joined Dara Costelloe in joining from Burnley, but Ryan Astley is still yet to make his debut after a move from Everton.
Hearts will remain without Australian duo Kye Rowles and Nathaniel Atkinson ahead of their quarter-final clash with South Korea in the Asian Cup this week.
As far as injuries are concerned, Cammy Devlin and Liam Boyce remain the only absentees for Naismith's side ahead of this trip.
Shankland's goal last weekend in the win over Aberdeen was his 14th of the campaign, as he remains clear at the top of the scoring charts and is still the first name on the Hearts team sheet.
Dundee possible starting lineup:
Carson; Ashcroft, Shaughnessy, Dodgson; McGhee, Boateng, Sylla, Cameron, Beck; Bakayoko, Robinson
Hearts possible starting lineup:
Clark; Lembikisa, Kingsley, Kent, Cochrane; Nieuwenhof, Baningime; Oda, Grant, Forrest; Shankland
We say: Dundee 0-2 Hearts
Results have been very varied between these two sides at Dens Park since Dundee's top-flight return in 2012, with the hosts 7-5 up in terms of wins in 13 meetings.