Chris Burke scored Rangers' winner just before half-time with a magnificent curling left-foot shot.
The match ended in drama though as, with ten minutes remaining, Rangers substitute Nacho Novo was sent off for a lunging two-foot tackle on Hibs' wing-back Thierry Gathuessi.
Gers manager Walter Smith was incensed by the reaction of his Hibs counterpart Mixu Paatelainen who wanted Novo sent off. Both managers squared up to each other with the referee, on the advice of the fourth official, ordering Smith to the stands.
Despite their extra man, Hibs were unable to create a clear-cut chance against a Rangers defence that was superbly marshalled throughout the match by Carlos Cuellar.
The game started quietly until Steven Whittaker fired in a powerful 25-yard shot which Yves Makaba-Makalamby palmed away.
The visitors responded with a splendid 30-yard shot from Steven Fletcher which Neil Alexander was happy to parry.
Burke came more into the match as the half wore on and, after a superb running cross by the winger, Chris Hogg just managed to block Lee McCulloch's net-bound shot.
Rangers took the lead in the 39th minute when Steven Davis sent a superb cross-field pass to Burke who cut inside Abderraouf Zarabi before flighting the ball beyond the reach of the Hibs keeper.
At this stage Hibs were down to ten men as Ian Murray was off the pitch having treatment for a facial knock and Rangers had great chances to increase their lead.
Makaba-Makalamby pulled off a magnificent block with his foot to deny McCulloch and then touched Steven Naismith's header onto the bar.
In a swift break Burke's pass put Naismith through on goal but again the Hibs keeper blocked his effort.
After their midweek European exertions, Rangers seemed prepared to defend their lead in the second half. Hibs came more into the match, but their attack lacked a cutting edge.
Indeed, Kevin Thomson nearly added to Rangers' lead but shot weakly at the keeper after Barry Ferguson's pass had put him through.
After Novo's dismissal, the nearest Hibs came to an equaliser was when substitute Abdessalam Benjelloun flashed an 18-yard shot narrowly over the bar.