Ten man Hearts picked up a vital three points at Dens Park with Claudio Braga's sensational first half strike enough to separate the sides on Tayside.
The Portuguese forward notched from distance to send the Jambos on their way, but Alex Schwolow's dismissal in first half stoppage time set up a nervy second half for Hearts with their backs to the wall.
Substitue Craig Gordon made a string of world class saves to maintain the lead, with stout defending from the boys in maroon enough to see Hearts over the line.
Derek McInnes made one change to the side from last time out; Jamie McCart slotting in at left-back for Harry Milne following an ankle roll in training, with new recruit Islam Chesnokov handed a spot on the bench in place of Stephen Kingsley who's dealing with a groin strain.
Dundee raced out the blocks and forced a save from Alex Schwolow in the Hearts goal with just over a minute on the clock; diving across to make a stretching save from Billy Koumeito's header via a Tony Yogane cross from the left.
The Jambos kept at it, and a good move petered out after 12 minutes when Claudio Braga knocked Craig Halkett's dinked ball into the path of Lawrence Shankland just inside the area - but skipper's deflected effort dragged wide.
With 26 minutes gone, the Jambos raced into a surprise lead after a competitive start. A quick free-kick found Shankland in space, who slid the ball across to Braga - who arrowed a delightful strike in off the post from distance to send the travelling support into raptures.
The men in maroon were in the ascendancy after this, and Lawrence Shankland was next to try his luck with a dig from distance after 35 minutes, seeing his spectacular strike swerve just past the post.
Two minutes later, the Jambos went again, and Alexandros Kyziridis went agonisingly close to a second after some cool link-up play with Jordi Altena - his low smash towards goal palmed away to safety by Jon McCracken.
There was to be a twist in the tale as the first half faced a dramatic end; with the Jambos reduced to ten men after a VAR check determined that Alex Schwolow had denied a Dundee goal scoring opportunity with the Dee through on goal.
Braga was sacrificed for Craig Gordon, with Scotland's number one called into action straight away as he made a magnificent reaction save to deny Dundee from the resulting free-kick.
HT: Dundee 0-1 Heart of Midlothian
The Jambos would have to play with their backs to the wall for much of the second half, but still had enough quality to threaten, with Lawrence Shankland seeing a header flash over the bar after 55 minutes courtesy of a Kyziridis delivery.
Hearts restricted Dundee for much of the second half, but the last ten minutes saw the Jambos fend off an onslaught, starting with Hamilton flashing a header over the crossbar.
Minutes later, Craig Gordon produced a phenomenal save from Drey Wright who found space at the near post, before wrapping up the points with a breathtaking save from Acquah in the final minute of stoppage time - stretching at full tilt to tip his header around the post.
Dundee: McCracken, Astley (Samuels 64'), Koumetio, Wright, Robertson (Murray 64'), Hay, Yogane, Congreve, Graham, Jones (Reilly 86'), Hamilton
Subs: O'Hara, Ingram, Robertson, Digby, Acquah, Samuels, Murray, Reilly, Bevan
Hearts: Schwolow, Halkett, McCart. Baningime, Shankland (Kabore 70'), Braga (Gordon 45+5'), Devlin, Findlay, Magnusson, Altena (Steinwender 45'), Kyziridis (Kent 70')
Subs: Gordon, Kent, Kabangu, Kabore, Steinwender, Spittal, Forrest, Kerjota, Chesnokov
