Inverness had beaten Rangers in Glasgow in mid-October but since then they had slid down to second bottom in the table and Paul Le Guen's men have been embroiled in a battle with Aberdeen for a Champions League berth.
Within seconds, Inverness hitman Graham Bayne had posed a threat when he beat the offside trap and saw his low drive easily gathered by Allan McGregor.
The hosts continued to press and a corner caused panic and Dennis Wyness was closed down as he threatened to pounce in the box.
The Highlanders were full of promise in the early stages but Rankin should have done better when put clear in the area by Barry Wilson.
Rangers' first opportunity came by way of a sixth minute free-kick but Charlie Adam steered it past the right-hand post.
Sasa Papac was then found out wide left and his tasty cross was headed over the top by Libor Sionko.
The visitors began to gain a grip on the game and Mark Brown did well to get down and hold a fierce Adam drive.
Out of nowhere, Rangers were given a golden chance to take the lead when skipper Barry Ferguson tumbled under a challenge from Roy McBain. Nacho Novo then steered the ball in the opposite direction of Brown from the penalty spot for a 1-0 scoreline.
Inverness almost hit back within minutes when Ross Tokely's driving run teed up Rankin, whose shot was touched away by McGregor.
They never gave up and got their reward a few moments from half-time when Rangers failed to clear their lines and central defender Darren Dods was the shock man in the right place to bury the chance for the leveller.
It was a really even affair for most of the second half and Rankin even hit the base of a post when he connected with a Wilson cross on 64 minutes.
McGregor then pulled off a terrific point-blank save from a well-taken swerving shot from the edge of the box.
The keeper then showed his class with two quick-fire saves from Wyness as Inverness went for the second.
Rangers then came more into the match and a decent Ferguson free-kick tested Brown with height but not enough power on 77 minutes.
Then in stoppage time a sensational searing run from Rankin ended with a superb 25-yarder into the roof of the net for a stunning winner.