Hearts substitute Dennis Wyness blasted home a superb volley 14 minutes from time to grab his side a share of the points.
And it was no more than the home side deserved after they went behind to a hotly disputed penalty.
Robbie Neilson was adjudged to have obstructed the flying Dane Peter Lovenkrands, but it was a very soft decision.
Gers skipper Craig Moore took the responsibility from the spot and slid home a low right-foot finish.
It was always going to take something special to beat Hearts' inspired keeper Craig Gordon.
The youngster made a handful of inspired saves at the end of the first half - tipping over Stephen Hughes' volley and Moore's header before saving at Lovenkrands' feet.
Stefan Klos had also saved Rangers with a terrific stop to deny Alan Maybury from 25 yards, but you felt Hearts would struggle to come back after Moore's penalty.
And only another fine save from Gordon denied Ronald de Boer a second after a mistake from Kevin McKenna.
But back Hearts came and the subs combined to grab the leveller.
Andy Kirk cushioned down a header and Wyness flashed a 15-yard volley beyond the dive of Klos.
And that was the signal for a grandstand finish from Hearts.
Incredibly, Joe Hamill screwed his shot wide with only Klos to beat from eight yards, before Moore headed a full-blooded drive from Neilson wide of the target.
Hearts also had a late penalty claim waived aside when Maurice Ross looked to have handled in the box, but in the end a draw was about right.