Rangers moved four points clear at the top of the Premier League thanks to a late goal from Jean-Claude Darcheville.
French striker Darcheville was the match-winner for Rangers
The substitute striker prodded a high ball home on 88 minutes, with the home defence slow to react.
Rangers' Charlie Adam clipped the crossbar from 20 yards and was denied a goal when Daniel Cousin was ruled offside inside the six-yard box.
Inverness came closest with a strike from Marius Niculae which was well saved by Allan McGregor.
It was a far from vintage performance from Walter Smith's side but, just as they did against Gretna on Wednesday, Rangers ground out a vital win away from home.
Inverness never looked like adding to their five-match winning run at home but will feel aggrieved after containing Rangers with relative ease for so long.
A subdued first half saw both sides moving the ball around without too much opposition and making little impression in the final third of the pitch.
After 15 minutes, Rangers striker Cousin muscled his way past a couple of defenders on the edge of the penalty box only to blaze his shot high over the crossbar.
And, ten minutes later, the home side threatened when Markus Paatelainen burst into the penalty area but goalkeeper McGregor got down smartly to block with his feet.
A cross to the far post from Rangers winger Chris Burke found Cousin but the Gabonese's header was comfortably gathered by the diving Michael Fraser.
Shortly before the interval, Rangers right-back Steven Whittaker got forward to collect a neat pass from Steven Naismith and his powerful strike was beaten away by Fraser.
The visitors threw on Darcheville in a bid to inject some life into their attack and he sent a scuffed effort straight at Fraser before Inverness midfielder Ian Black tried his luck with a tame long range shot.
Darcheville then sent a rising strike narrowly over the crossbar, while Adam looped a dangerous first-time strike in the same direction.
Inverness striker Niculae had been starved of service but found room for a rasping shot from 25 yards on 68 minutes and McGregor was at full stretch to keep it out.
Adam thought he'd scored when he curled in a shot from a narrow angle but Cousin was flagged offside.
The same player was denied on 83 minutes when he crashed a fantastic strike against the crossbar.
However, Rangers found a way through when the home side failed to deal with a high, hopeful ball into the box and Darcheville was able to steer it home from 12 yards out.
Inverness were given a glimpse of goal in injury time but defender Ross Tokely thrashed the ball wildly off target.
Inverness CT: Fraser, Tokely, Proctor, Munro, Hastings, Cowie, Black, Duncan, McBain, Paatelainen (Wilson 69), Niculae. Subs Not Used: Malkowski, Bayne, Wyness, Vigurs, Gillespie, Duff.
Rangers: McGregor, Whittaker, Cuellar, Weir, Papac, Burke, Ferguson, Hemdani, Adam, Naismith (Darcheville 46), Cousin (Novo 75). Subs Not Used: Graeme Smith, Boyd, Broadfoot, Lennon, McMillan.
Goal: Darcheville 89.
Ref: C Richmond