Inverness might have started the day at the bottom of the SPL, but they certainly did not play like a side struggling in the relegation zone.
With Rangers finding it difficult to exert any pressure, Caley Thistle took heart from a solid start and only a wonderful reaction save by Allan McGregor to keep out Iain Vigurs' header kept parity in the scoreline with 17 minutes gone.
Nine minutes later, Don Cowie tried his luck from the edge of the box, but McGregor managed to scramble the ball away before it was cleared to safety.
Rangers had to wait until the 31st minute to register their first shot on target, Steven Davis firing a volley straight at goalkeeper Ryan Esson after Kenny Miller had attempted to force his way through the home defence.
Vigurs was proving to be a thorn in the visitors' side and two minutes before the interval he was inches away from giving Caley a lead they would have merited.
Taking time to compose himself from 25 yards, he sent in a shot that had McGregor at full stretch only for the effort to ruffle the sidenetting.
All Caley Thistle's good work was undone, however, only 23 seconds into the second half as Pedro Mendes curled home a exquisite effort from 25 yards that would once more mean Inverness still had not kept a clean sheet since the opening day of the season.
The hosts attempted to respond, but Andrew Barrowman could only head a Don Cowie cross high over the crossbar from eight yards.
Kris Boyd has been in fine form for Rangers of late and he was so nearly on target again, collecting sub Chris Burke's pass before sending in a low shot that was gathered at the second attempt by Esson.
Barely 60 seconds later, Esson had to look lively again, this time preventing Ross Tokely from putting through his own net from a Mendes cross.
The home goal was now coming under siege, Davis the next to try his luck with a shot from 20 yards that landed on the roof of the net.
The introduction of Burke had at least given Rangers more width and he came close to putting the game beyond Inverness with a superb run and shot that flew narrowly wide of the post.
It was now real end to end stuff and after McGregor had parried away Barrowman's shot, Rangers made it 2-0 with nine minutes remaining.
Davis picked out the run of Boyd with a well-weighted pass and the prolific striker did the rest by firing low into the corner of the net for his 19th of the season.
The former Scotland international then moved his tally on to 20 six minutes later, heading home Burke's cross at the back post.
By then, however, the game was all but over as Rangers breathed new life into their title challenge with this win in the Highland Capital.