An opportunist goal from Derek Riordan late in the first half was enough to give Hibs all three points.
Riordan turned in a shot from Kevin Nicol for the only goal of a tepid encounter at Easter Road.
Nacho Novo had a chance for Dundee after just two minutes but his angled shot was beaten out by Daniel Andersson.
But Hibs hit back and a Riordan cross picked out Scott Brown at the back post but his shot lacked power and Julian Speroni saved easily.
But the Dundee goalkeeper had to produce a breathtaking save to keep his side level after 17 minutes.
A quick free-kick from Nicol had the Dundee defence in disarray and Brown cut the ball back for Tom McManus to fire in a shot on the run.
But Speroni somehow managed to leap across his goal and divert the ball to safety.
Dundee went close at the other end when Colin Murdock was caught out by Novo but the striker's shot struck the base of the post with Andersson beaten.
Novo had another opening in the 39th minute when he beat Gary Caldwell to set up a shooting chance but he miskicked with the goal at his mercy and sliced his shot wide.
Dundee paid the price and Hibs took the lead two minutes later. A McManus corner was headed on by Murdock and Nicol's 16-yard shot was turned in by Riordan.
Dundee had most of the possession in the second half but rarely put Andersson under any pressure.
Caldwell cleared a Novo shot off the line but it was Hibs who should have extended their lead in injury-time.
Substitute Stephen Dobbie beat Speroni with a terrific shot but it thumped against the crossbar.
Riordan picked up an ankle injury in the final moments but caretaker-manager Jim Clark confirmed it was not serious.