Pressure mounted on Rangers manager Alex McLeish after the Scottish champions slipped up again despite Caley Thistle finishing with 10 men.
Craig Dargo gave Inverness a surprise lead with a 25-yard volley.
Fernando Ricksen struck the visitors' bar before substitute Steven Thompson pounced after goalkeeper Mark Brown spilled a cross after the break.
Rangers pressed for a winner and Graham Bayne was sent off late on for a bad challenge on Peter Lovenkrands.
McLeish had made two changes after the midweek draw at Livingston.
Bob Malcolm replaced the injured Jose-Karl Pierre-Fanfan in the heart of the defence, with Alan Hutton at right back and Ian Murray dropping on to the bench.
Inverness made five changes from the side that lost to Falkirk, with Dargo, Bayne, Richard Hastings, David Proctor and Ian Black all drafted in.
The revamped Caley Thistle were under early pressure and Lovenkrands burst into the box before unleashing a shot across the face of goal.
Hutton headed over from just inside the Inverness area, but Rangers were left reeling when Inverness took the lead in the 26th minute.
A long ball from Brown was collected by Dargo and he sent a superb first-time dipping volley past home goalkeeper Ronald Waterreus from 25 yards.
Luck was not on Rangers' side as they tried to reply, a stinging Marvin Andrews effort hitting the body of team-mate Dado Prso on the way to goal.
And a Ricksen header smacked off the crossbar.
McLeish replaced Chris Burke with Thompson at the break and the Scotland striker struck the equaliser nine minutes into the second half.
Brown jumped above everyone else but failed to hold a Hutton cross.
It broke to Thompson and he hooked the ball over the line from close range.
The crowd were on their feet again when Prso connected just outside the six-yard box only to send his header screaming past the post.
Rangers were threatening again when Lovenkrands met a Ricksen corner only for his cheeky back-flick to be blocked on the line by Alan Morgan.
Lovenkrands embarked on an astonishing 75-yard run before going to ground under pressure from Darren Dods.
But referee Iain Brines was unimpressed by his efforts and no penalty was given.
Graham Bayne was shown his second yellow of the day.
But Caley Thistle survived late pressure as Rangers were jeered from the field once more.
Rangers: Waterreus, Hutton, Malcolm, Andrews, Bernard, Ricksen, Ferguson, Hemdani, Burke (Thompson 45), Prso, Lovenkrands.
Subs Not Used: Klos, Alex Rae, Murray, Namouchi, Smith, McCormack.
Booked: Hemdani, Ricksen, Malcolm.
Goal: Thompson 54.
Inverness CT: Brown, Tokely, Dods, Munro, Hastings, Duncan, Black, Proctor, Morgan, Bayne, Dargo (Wyness 85).
Subs Not Used: Fraser, McCaffrey, Hart, Juanjo, Parratt, Fox.
Sent Off: Bayne (82).
Booked: Black, Bayne, Dargo, Tokely.
Goal: Dargo 26.
Ref: I Brines