A double from Garry O'Connor and goals from Steven Whittaker and Steven Fletcher gave them their seventh victory in their last eight matches at Easter Road. Dundee never seriously looked like pulling it out of the fire and too often their finishing let them down.
Dundee had a chance in the opening minute when Steve Lovell rounded Simon Brown but the angle was too tight and his effort was cleared by Whittaker. Fabian Caballero then had an opportunity when Whittaker loitered on the ball, but again the angle was tight and Brown saved comfortably
It did not take Hibs long to get into their stride. A superb pass from Stephen Glass picked out Sam Morrow but, as the striker was about to pull the trigger, Stephen Robb managed to make the blocking challenge.
Then a Derek Riordan free-kick came off the wall and dropped on to the head of Steven Fletcher, but Derek Soutar was well positioned to save.
Moments later O'Connor robbed Lee Wilkie on the left and drilled a shot against Soutar, but Dundee cleared before Fletcher could pounce on the rebound.
The Hibs' breakthrough came after 26 minutes. O'Connor's pass fell to Riordan and when Soutar pushed out his effort, the alert O'Connor was ideally positioned to stroke home the ball at the far post.
Dundee had chances to pull level before half-time. Former Hibs player Tom McManus was put through by Caballero, but his right-foot shot was tame and Brown saved comfortably. McManus then tried his luck with a well-struck free-kick which beat the wall but was directed straight at Brown.
Hibs extended their lead after barely a minute of the second half with a well-worked goal. Whittaker played the ball out to O'Connor who cut the ball back into his path, and he rifled a 10-yard shot into the roof of the net.
The goal encouraged Dundee to open up more and McManus created a chance for Lovell with a neat cutback, but the striker sliced his shot well wide. Neil Barrett then looped a header just a yard too high from a Callum MacDonald cross.
Substitute Scott Brown then set up the third 15 minutes from time with a cross from the right which Fletcher headed beyond Soutar.
O'Connor grabbed the fourth with a fine left-foot finish two minutes later as Dundee caved in.