Dundee handed three players their first home start this afternoon with Craig Burley, Callum McDonald and Robert Linn coming into Jim Duffy's injury-ravaged side.
The home team had loud penalty claims turned down when Linn tumbled into the box with six minutes played.
A fierce 30-yard drive by Derek Riordan was well held by Julian Speroni moments later.
Dundee almost went ahead with 20 minutes played but Fabrizio Ravanelli's diving header from Nacho Novo's cross was turned onto the post by Daniel Andersson in the Hibs goal.
Dundee were dealt a major blow midway through the first half when Craig Burley was ordered off for a wild tackle on Tom McManus.
The Dark Blues regrouped, however, and ten minutes later they took the lead when top scorer Novo knocked home Ravanelli's knock down from two yards.
Stephen Glass surprised Speroni with a fierce left-foot shot that the keeper gathered at the second attempt on the stroke of half time.
Garry Brady saw his low left-foot effort well saved by Andersson seven minutes into the second half.
Dundee skipper Barry Smith was unlucky when his curling shot was brilliantly saved by Andersson with just over an hour played.
Seconds later, Speroni dived full length to deny Riordan at the other end.
Just 15 minutes from time, Hibs substitute Stephen Dobbie missed a glorious chance to equalise when a great run and cross by Riordan found him at the back post but from three yards out and all alone he put the ball past the post.
The visitors did get the equaliser with nine minutes remaining when Riordan curled a 25-yard free-kick in off the post.
Novo was clean through on goal with four minutes to go but the little striker was blocked by a combination of Andersson and Mathias Doumbe.
The visitors should have grabbed the winner two minutes into stoppage time, but to the dismay of their fans Ian Murray headed over when unmarked four yards from goal.