A Dado Prso penalty gave Rangers a precious victory in the battle of the 10 men at Hibernian's Easter Road.
The odds had been against Alex McLeish's men when Nacho Novo was shown a straight red card in the 28th minute for kicking Craig Rocastle.
But Gary Caldwell was dismissed after the break for fouling Hamed Namoucho and Prso made no mistake from the spot, although he did miss a later penalty.
The result leaves Rangers four points adrift of leaders Celtic, having beaten them this week in the most recent Old Firm derby, with the next meeting to take place next weekend at Ibrox.