This was a shocking display by Rangers but it looked as though a Barry Ferguson goal after the break was enough to give them victory.
There was no doubt that Inverness deserved their share of the points even if their equaliser did not arrive until the last minute.
This result was a fair blow to Rangers' championship hopes. Even though the home side are still seven points ahead Celtic have three games in hand and the advantage is now with the Parkhead side.
Nacho Novo made a break in the early stages but his cross fell behind Steven Thompson, before Rangers wasted another good chance when Thompson headed wide from a Bojan Djordjic cross.
The visitors had a great chance to take the lead when Stuart Golabek's shot deflected off Marvin Andrews to Ross Tokely, but his shot drifted just wide.
Ferguson broke into the box and appeared to be brought down from behind by Golabek but the ball broke to Novo, whose shot was blocked by Mark Brown.
Rangers looked lethargic with Ferguson and Fernando Ricksen unable to dominate the midfield and Juanjo threatened on a number of occasions before the interval.
The home team looked sharper after the break and Thomas Buffel's pass gave Novo room in the box, but his short was smothered by Brown at the near post.
Ricksen shot high over before Novo pulled his effort wide as Rangers at last applied some pressure.
The breakthrough arrived when Ricksen's pass released Ferguson, who skilfully lobbed Brown from the edge of the box to put his side ahead.
A brilliant run by Andews ended with a pass to Buffel, whose shot was saved at full stretch by Brown.
Rangers keeper Ronald Waterreus then produced a marvellous double save to keep out efforts from Juanjo and Bejram Fetai in a goalmouth scramble.
Novo should have wrapped up the points when he was clean through on goal but Brown did well to turn his shot behind.
Caley Thistle equalised when Golabek's long ball hit Sotirios Kyrgiakos in the back and Bryan Prunty was on hand to shoot home beyond Waterreus.
Rangers may bitterly regret the loss of these two points when the honours are decided at the end of the season.