A breathtaking first-half display from the home side was garnished by goals from Derek Riordan and Garry O'Connor, but Rangers fought back in the second half to belatedly make a contest of it.
A deflected goal from Barry Ferguson gave them some hope, but Hibs held on for their first home win over Rangers for five years.
Ferguson's afternoon ended in misery as he was sent off in injury-time for his second booking.
Rangers gave Ross McCormack a starting role after his heroics against FC Porto in midweek, but it was Hibs who made the early running as Rangers struggled to cope with the pace of Ivan Sproule.
Sproule, who hit a hat-trick at Ibrox earlier in the season, saw an early shot blocked before O'Connor steered a header at Ronald Waterreus when he should have done better.
Rangers were overrun in midfield and Riordan shot home the opener after 17 minutes with a simple goal after Sproule had cut the ball back into his path.
Alex McLeish tried to change it and replaced Alex Rae with Brahim Hemdani after just 24 minutes.
But, within a minute, Hibs were two up after a wonderful goal. This time Riordan turned provider as he swept over a cross and O'Connor beat Waterreus with a stunning volley.
Rangers offered little in response in a poor first half and the ineffective Francis Jeffers was replaced at half-time by Steven Thompson.
Riordan had a chance to add to Hibs' lead early in the second half but Waterreus had his angles covered.
Another terrific run from Sproule had Rangers stretched again but he pulled his final shot just inches wide.
But Rangers pulled one back out of the blue when a Ferguson shot was deflected off Gary Caldwell into the net.
Hamed Namouchi should have equalized but lacked composure when he lashed the ball over from just eight yards.
A poor header from Marvin Andrews gave Sproule another chance late on but he shot straight at Waterreus.
Then came Ferguson's red card on an afternoon Rangers will want to forget.