Rangers left Easter Road with all three points thanks to a Dado Prso penalty against a Hibs side that dominated much of the game but could not score.
Nacho Novo was sent off for kicking Craig Rocastle after 28 minutes but Hibs failed to capitalise.
Rangers went ahead from the spot after Gary Caldwell pulled Hamed Namouchi down and the Hibs man was red-carded.
Prso missed a second penalty in the 90th minute and Ian Murray hit the post as Rangers held out for the victory.
Hibs started the match at great pace and their slick passing combined with tremendous tenacity in the tackle had Rangers on the back foot for much of the opening half-hour.
Nonetheless it was Novo who might have got the first goal when he burst free down the right, but his shot from a tight angle went narrowly wide, with the unmarked Prso left cursing his strike partner for choosing not to pass.
Garry O'Connor came closer still when he beat Jean-Alain Boumsong before lobbing the ball over Stefan Klos, only to see it come off a post and bounce clear.
Klos kept his side level moments later when Derek Riordan whipped in a wicked cross, which Guillaume Beuzelin got a slight touch to, but the keeper reacted quickly to push the ball away.
Hibs' cause was aided when Novo's petulant kick at Rocastle was spotted by the referee's assistant and Willie Young showed the Spaniard a straight red card.
Lovenkrands ought to have done better with a close-range header that Simon Brown held comfortably but Hibs' dominance diminished following Novo's dismissal.
They remained on top into the second half and Rocastle sent a fierce drive just wide from outside the box.
But the balance of play shifted after 63 minutes when Caldwell brought Namouchi down as he prepared to shoot from eight yards out.
Caldwell trots off after his red card
The Hibs defender was ordered off and Prso sent the resultant penalty past Brown.
Substitute Jamie McCluskey shot well over the bar as Hibs tried to claw their way back into the game.
As full time drew closer, Namouchi brought a fine save from Brown and a powerful Bob Malcolm shot went just wide before Prso was handed the opportunity to seal the victory from the spot.
Murray pulled Fernando Ricksen down but Prso hit the outside of the post with his effort.
In the closing moments, Murray directed a header against the base of Klos' post and Rangers held on for the win.
Hibernian: Simon Brown, Whittaker, Caldwell,
Murdock (McCluskey 70), Glass, Shiels, Rocastle (Smith 65),
Beuzelin, Murray, O'Connor (Morrow 65), Riordan.
Subs Not Used: Alistair Brown, Fletcher, Murphy, Orman.
Sent Off: Caldwell (63).
Booked: Shiels, Simon Brown, Smith.
Rangers: Klos, Khizanishvili (Hutton 82), Andrews, Boumsong,
Ball, Namouchi, Ricksen, Malcolm, Lovenkrands (Alex Rae 45),
Subs Not Used: Graeme Smith, Arveladze, Vanoli, Hughes,
Sent Off: Novo (28).
Goal: Prso 65 pen.
Ref: W Young