Derek Riordan and Garry O'Connor fired Hibernian to victory as Rangers went eight games without a win for the first time in their 132-year history.
Ivan Sproule set up Riordan for a simple tap in after 18 minutes.
Riordan turned provider seven minutes later, his cross being side-footed home from 16 yards by O'Connor.
A Barry Ferguson drive deflected in off Gary Caldwell, but Rangers' captain was sent off for a second yellow to heap more pressure on boss Alex McLeish.
Yet the title holders, now 11 points adrift of third-top Hibs, had gone into the game hoping to build on their Champions League draw away to Porto.
They had been forced to rest Fernando Ricksen, who had been struggling from a muscle strain, but midweek substitute heroes Ross McCormack and Chris Burke started along with fellow youngster Alan Hutton.
Fit-again Gary Smith had replaced Chris Hogg at the heart of the Hibs defence, while Spoule came in for the injured Michael Stewart in midfield.
And Sproule's renowned speed immediately troubled the Rangers defence, former Hibs defender Ian Murray having to head away the winger's cross-cum-shot clear of goal.
Murray blocked another effort from Scott Brown and O'Connor headed straight at goalkeeper Ronald Waterreus from 15 yards.
A great ball out of defence from Guillaume Beuzelin set up the opening goal.
Sproule sprinted clear of Hutton and the Northern Irishman slipped the ball wide of Waterreus and into the path of Riordan to fire home at the back post from five yards.
Hemdani replaced Alex Rae after 24 minutes, moments after the veteran midfielder was booked.
Matters immediately got even worse for Rangers when Riordan found O'Connor superbly with a cross into the box and the Scotland striker neatly side-footed the ball into the corner of the net from 16 yards.
McLeish withdrew the ineffectual Francis Jeffers at the break, the on-loan striker being replaced with Steven Thompson.
Rangers pulled one back with their first shot on target, Ferguson's low drive from the edge of the box deflecting over Zbigniew Malkowski.
Hamed Namouchi should have equalised but blasted over from 10 yards after Malkowski failed to collect a cross under pressure from Marvin Andrews.
A curling Riordan free kick slipped just wide and Waterreus saved superbly from Sproule as desperate Rangers were caught on the break.
And their chances were killed off when Ferguson was sent off in the dying seconds.
Hibernian: Malkowski, Whittaker, Smith, Caldwell, Glass, Sproule, Thomson (Shiels 90), Scott Brown, Beuzelin, Riordan (Morrow 88), O'Connor (Fletcher 75).
Subs Not Used: Simon Brown, Hogg, McDonald, Rudge.
Booked: Scott Brown, Beuzelin.
Goals: Riordan 18, O'Connor 25.
Rangers: Waterreus, Hutton, Andrews, Kyrgiakos, Murray, Burke (Lovenkrands 60), Ferguson, Alex Rae (Hemdani 24), Namouchi, Jeffers (Thompson 46), McCormack.
Subs Not Used: Klos, Malcolm, Pierre-Fanfan, Smith.
Sent Off: Ferguson (90).
Booked: Alex Rae, Ferguson.
Goal: Ferguson 59.
Ref: S Dougal