Second-half goals from Callum Paterson and Bjorn Johnsen secured a deserved victory for Hearts in an exhilarating encounter at Tynecastle that was littered with goal-scoring chances at both ends.
The hosts dominated the first half but were frustrated by a combination of missed chances and some outstanding saves from Dundee goalkeeper Scott Bain.
Ironically, Hearts' breakthrough came at a time when the visitors, who started the second period strongly and hit woodwork four times in total, were threatening to take the lead.
Hearts made two changes to the side that won at Motherwell a fortnight earlier, as Don Cowie and Alim Ozturk, making his first league start of the season, came in for injured pair Sam Nicholson and Faycal Rherras.
Dundee had a great chance within seconds of kick-off when Callum Paterson's slack pass was intercepted by Faissal El Bakhtaoui but John Souttar got back to make a fine tackle on the Moroccan just as he looked set to pull the trigger inside the box.
Paterson was involved at the other end in the fifth minute when his inswinging cross from the right almost dipped in at Scott Bain's far post.
The hosts were on top in the early stages and Conor Sammon was put clean through on goal in the seventh minute after Jamie Walker dispossessed Dundee centre-back Kevin Gomis but Bain made a fine save to deny the Irish striker.
Two minutes later Paterson cut in from the right and rifled a low left-footed shot from the edge of the box just wide before Watt glanced a header over the top from a dangerous Don Cowie cross.
Hearts were seemingly creating chances at will in the early stages and another came their way in the 15th minute when Sammon dispossessed Danny Williams and crossed for Watt, but the striker blazed high over from a great position.
The pressure subsided temporarily and Tom Hateley almost gave Dundee the lead in the 20th minute when his free-kick from just outside the box clipped the top of the par.
The hosts were soon on the front foot again and Paterson rasped a shot just past in the 23rd minute after Watt's cross from the left broke kindly to him just outside the box.
Cowie then fired over the top after playing a one-two with Watt on the half-hour mark.
Hearts should have gone ahead in the 31st minute when Sammon's determination down the right allowed him to cross for Watt but the hitman's goalbound effort from ten yards out was inadvertently blocked by team-mate Walker.
Seconds later a tantalising Paterson delivery from the right flashed beyond the far post, with Sammon and Walker somehow unable to get a decisive touch in the middle.
Four minutes before the break, Arnaud Djoum saw a low left-footed shot from the edge of the box brilliantly tipped behind by Bain. From the resulting corner, taken by Cowie, Paterson's header was well saved by the goalkeeper as Hearts somehow went in at the interval without a goal to show for their dominance.
Dundee almost went ahead two minutes after the break when Hateley smacked a half-volley against the post from the edge of the box. The visitors threatened again three minutes later when El Bakhhtaoui's low drive from 20 yards out was brilliantly clawed behind by Jack Hamilton. From the resulting corner, taken by Hateley, Kostadin Gadzhalov headed against the crossbar.
At the other end, Walker was denied by Bain from ten yards out after good work by Watt and Djoum to set him up.
Hearts made their first change of the match after 57 minutes when Robbie Muirhead replaced Watt. The home support booed the decision to take off the former Celtic striker.
Dundee struck woodwork in the 62nd minute when Yordi Teijsse's shot from the edge of the box came back off the post.
In a game which had been full of chances at both ends, Hearts eventually made the breakthrough in the 68th minute when Muirhead's magnificent free-kick from wide on the left was met by Paterson, who bulleted a firm header beyond Bain and into the net.
Substitute Johnsen almost added a second for the hosts with seven minutes left but Bain made a sensational reflex save to block the American's close-range effort.
At the other end, Teijsse flashed a free header just past from a few yards as the visitors threatened a late fightback.
But Johnsen eased the nerves of the home support in the 89th minute when he met a low Walker cross at the front post and clipped home his first goal for the club.
Hearts: Hamilton, Paterson, Rossi, Ozturk, Souttar, Kitchen, Djoum, Cowie (Buaben 86), Walker, Watt (Muirhead 57), Sammon (Johnsen 71). Unused subs: Noring, Oshaniwa, Nowak, Currie.
Dundee: Bain, Hateley (Kerr 76), Gomis, Gadzhalov (Loy 85), Holt, McGowan, O'Hara, Vincent (Duffy 76), Williams, Teijsse, El Bakhtaoui. Unused subs: Gourlay, Etxabeguren, Ross, Wighton.
Ref: Kevin Clancy