Nacho Novo gave Rangers the lead from the spot midway through the first half, but Darren Dods equalised just before the break to bring the sides level.
With one change to the starting line-up – Filip Sebo in for the injured Dado Prso – Rangers continued with the 4-4-2 formation that has served them so well in recent games.
Despite the ungodly kick off time, enforced due to television rights, Paul Le Guen’s side appeared well up for the challenge at the Caledonian stadium.
Although it was Inverness who created the best early chances, Rangers soon warmed up and started to cause their own problems.
Within the first minute Graham Bayne tested Allan McGregor with a low shot from the right, after Ian Black’s pass over the top deceived the visiting defence.
Two minutes later Dennis Wyness was caught on his heels inside the six yard box, when he failed to react to Roy McBain’s corner flick on and McGregor smothered.
McBain himself was then allowed acres of space to get an effort on goal, but blasted his shot high over the bar.
It was three real warnings to Rangers and they finally dragged themselves into the match after seven minutes.
Charlie Adam won a free kick in front of goal and although he drilled the ball wide, it sparked Le Guen’s side into life.
Libor Sionko, so effective down the right in the last game against Aberdeen, tried his luck when he cut inside but again couldn’t test Mark Brown.
After 10 minutes Barry Ferguson started to push further forward and he chipped a delightful ball over the top for Sebo, but he too fired over the bar.
Desperate for a goal, the Slovakian again burst clear to collect Jeremy Clement’s long ball forward and this time Brown saved well, before also blocking Novo’s follow up.
Within a 10 minute period Rangers had managed to turn this match around and at this point they had the bit between their teeth.
Sasa Papac burst down the left and whipped in a fine cross for Sionko, but his header dropped onto the roof of the net.
With quarter of an hour gone Ferguson did well to reach the by-line and cut the ball back to Novo, who then laid off Adam on the edge of the area, but his weak shot didn’t trouble Brown.
Six minutes later it was Ferguson’s running again that finally created the breakthrough for Rangers.
He sprinted beyond the strikers and when Adam’s pass picked out the skipper in the box, McBain’s touch was enough to stop him in his tracks and Charlie Richmond awarded the penalty.
Nacho Novo duly stepped up and sent Brown the wrong way to give the Light Blues the lead.
On 26 minutes Inverness tried to hit back when Ross Tokely’s low cross from the right found John Rankin unmarked and McGregor produced an excellent save to keep his side ahead.
Buoyed by his recent goal against Partizan Belgrade, Alan Hutton tried his luck with a powerful long range shot but the former Ibrox keeper watched it all the way and held well.
Five minutes from the break, however, Inverness struck back through Darren Dods.
The Light Blues failed to clear a corner and after a goalmouth scramble the ball broke to the home captain and he stabbed it past McGregor.
After 56 minutes Adam clipped a great diagonal cross into the box for Sionko but instead of shooting, when he had a clear eye on goal, he crossed for Novo allowing Dods to intercept.
At the other end Inverness came close to adding to their tally too when Rankin collected Wilson’s low cross and could only watch on as the post kept out his shot.
McGregor had to be at his best again on 69 minutes to deny Ian Black, who curled an excellent shot goalbound.
The young keeper proved his worth even more so with 19 minutes remaining when he pawed Wyness’ shot away and then smothered Inverness’ second effort.
Chris Burke was introduced to the game after 72 minutes for his first appearance since September 23.
For his first involvement he blasted a cross high over the bar, but then linked up well with Ferguson to release Novo down the right and Sebo was unlucky not to nip in ahead of Brown to score.
On 76 minutes Rangers won a free kick 30-yards out and the captain curled a fine effort up and over the wall, but the Inverness keeper held well.
Young midfielder Steven Lennon was given his debut as Gers tried to grab a winner, but it just wouldn’t come for Le Guen’s side.
In fact the match went full circle and it was Charlie Christie’s side who finished the stronger and snatched a winner in the first minute of injury time.
Rankin picked up the ball in midfield and drove forward unchallenged before launching a dipping shot over McGregor and into the net.
INVERNESS CALEY THISTLE: 4-4-2: Brown, Tokely, Dods, McBain, Rankin, Wilson (Morgan 77), Black, Munro, Hastings, Wyness, Bayne
SUBS: Fraser, McCaffery, Duncan, McSwegan, Sutherland, McAllister
BOOKINGS: Hastings 58, Black 78
RANGERS: 4-4-2: McGregor, Hutton, Svensson, Hemdani, Papac, Sionko (Burke 72), Ferguson, Clement, Adam, Novo (Lennon 83), Sebo
SUBS: Klos, Murray, Rae, Stanger, N’Diaye,
BOOKINGS: Clement 63, Hutton 42
REFEREE: Craig Thompson
ATTENDANCE: 7, 522