Hibs dominated early on and should have taken the lead after 10 minutes when Lee Wilkie was dispossessed by Garry O'Connor at the edge of his own area.
The Hibs striker had time to pick his spot but sent his shot against the post before Dundee scrambled the ball clear.
Six minutes later, slack play from Fabian Caballero gave Alen Orman a shooting chance but he directed his effort straight at Derek Soutar.
O'Connor had another chance from a Derek Riordan cross but looped his header over the top with the Dundee defence missing.
The lively Riordan gave Dundee an uncomfortable afternoon and he lashed a volley narrowly over the top late in the first half after more good work from O'Connor.
Dundee had an opening at the end of the first half when Lee Wilkie nudged the ball on for Steve Lovell, but Simon Brown was alert to the danger to cut down the striker's options and the chance was lost.
O'Connor had another decent chance early in the second half after being put through by Stephen Glass, but he pulled his shot wide with only Soutar to beat.
Dundee came more into things in the second half and Simon Brown had to get down well to keep out a Scott Robertson volley.
But Whittaker struck in the 75th minute from a pass from Jamie McCluskey and Hibs sealed the win three minutes from time.
Substitute Sam Morrow beat Soutar from a tight angle and there was no way back for Dundee.