A second-half penalty from Dado Prso was enough to give Rangers a narrow victory in a volatile match at Easter Road.
Prso struck midway through the second half but also missed a penalty in the final minute.
It was almost costly as Ian Murray hit the post with a header in injury-time.
Rangers had to play for more than two-thirds of the game with ten men after Nacho Novo was sent off after aiming a kick at Craig Rocastle off the ball.
Referee Willie Young missed the incident but it was drawn to his attention by assistant Steve Craven, although television pictures showed it was a soft ordering off.
Scotland defender Gary Caldwell followed Novo in the 64th minute when he was sent off for pulling down Hamed Namouchi when he was the last defender before Prso shot home the winning penalty.
Rangers were looking to follow up their midweek win over Celtic and were on top in the early stages.
But for all their possession, Rangers could not trouble a well organized Hibs defence.
Novo had a good opening when he sprinted clear in the 16th minute but lashed his effort across the face of the goal with Prso unguarded in the centre.
But Hibs responded and enjoyed the upper hand for the remainder of the half. Colin Murdock sent a header over before Garry O'Connor came within inches of opening the scoring.
He pounced on a terrific pass from Derek Riordan to lob the ball over the advancing Stefan Klos but the ball struck the post and bounced to safety.
Guillaume Beuzelin kept up the pressure with a long-range shot with his left foot that was well over.
Klos had to react swiftly to divert a shot from Riordan for a corner in a crowded goalmouth.
Then came Novo's sending-off which left Rangers short-handed after 27 minutes but they managed to withstand some heavy pressure from Hibs for the remainder of the half.
Rangers managed to create a chance of their own when Jean-Alain Boumsong outjumped the Hibs defence but his header was off target.
Rocastle came close again for Hibs early in the second half with a superbly-struck shot from the edge of the area which flashed narrowly wide.
Hibs bombarded the Rangers goal after that and Beuzelin set up another shooting chance for Rocastle and the midfielder was just a couple of yards wide with his effort.
But, against the run of play, Rangers took the lead after 64 minutes when Namouchi was pulled down by Caldwell when he was clean through which resulted in a penalty and a red card.
Prso made no mistake from the spot-kick to give Rangers a lead they hardly deserved.
Hibs tried to get back and substitute Jamie McCluskey swiped a shot over after good work by Steven Whittaker.
But Rangers wasted a great chance to double their advantage in the final minute when Murray fouled Fernando Ricksen in the area but Prso's penalty this time struck the post.
In injury-time, Murray headed a McCluskey cross against the woodwork and the final chance was gone.