Nikica Jelavic missed the clash at Ibrox through illness but skipper Steven Davis claimed a double and David Healy and Sone Aluko grabbed a goal apiece against 10-man Hibs.
With rivals Celtic in Scottish League Cup action this weekend, the victory allowed Rangers to give their title hopes a much-needed boost.
They made one change from the side who drew with Aberdeen at the same venue last week.
With Jelavic absent, Gregg Wylde was drafted into the side, while new signing Mervan Celik was named on the bench.
Hibs were without suspended duo Leigh Griffiths and Garry O'Connor, while James McPake - later sent off - and Tom Soares made their debuts from the start.
Rangers had an early chance to take the lead when Carlos Bocanegra saw his header blocked and the ball fell for Aluko, whose shot cannoned off McPake, who was wearing the captain's armband for the visitors.
Aluko then attempted to turn provider and released Lee Wallace through on goal but he was flagged offside before unleashing the shot.
At the other end, Soares threaded into the path of Eoin Doyle but Kyle Bartley came to the rescue with a timely tackle before the Hibs forward could shoot.
Rangers looked more likely to find the back of the net and Maurice Edu was not too far away when he collected a cut-back from Aluko and sent a powerful strike fizzing just past the post.
The home side's pressure paid off as they opened the scoring after 27 minutes when Davis raced onto an Aluko ball and rifled past the grasp of goalkeeper Mark Brown.
Rangers could have doubled their lead moments later when Edu had another go from distance but, again, was off target with a well-struck shot, before Wylde sent a free-kick just over the crossbar shortly before half-time.
Hibs emerged for the second half determined to haul themselves back into the game and Ivan Sproule burst down the left flank before squaring for David Wotherspoon but he was unable to connect in front of goal and the chance was lost.
Their hopes of a comeback were dealt a blow when Rangers doubled their advantage after 55 minutes.
Healy pounced on a long ball from Sasa Papac and took advantage of a mix-up in the Hibs defence to stroke home from the edge of the box with goalkeeper Brown off his line.
The home fans then screamed for handball against McPake but no penalty award was forthcoming from referee Charlie Richmond, before Edu's thunderous effort crashed off the post.
With 64 minutes gone, Rangers threw Celik into the action to make his debut.
However, it proved to be a maiden bow to forget for McPake who was shown a second yellow card for a challenge on Edu after 71 minutes, with the American midfielder quickly withdrawn for Lee McCulloch.
The match took a further turn for the worse for the Edinburgh club when Rangers netted their third of the day from the resulting free-kick a minute later.
Aluko had been instrumental in much of the game and was rewarded with a goal of his own when he sent a curling effort into the top corner, leaving Brown with no chance.
Davis then put the gloss on the win deep into injury time when he drove home from 10 yards to claim a double.