Celtic play host to Aberdeen on Sunday and all the attention will switch to Glasgow's East End in search of another twist in the title challenge.
Rangers broke the deadlock with an early goal from Thomas Buffel. A fantastic run from Nacho Novo, in which he twisted past three defenders, led to his effort being cleared off the line by Andy Webster. However, the ball fell nicely for Buffel and he cleverly placed his shot into the bottom right hand corner of Craig Gordon's net.
Hearts fought back and Paul Hartley's clever free-kick on 18 minutes was excellently tipped around the post by Ronald Waterreus.
Gordon denied Dado Prso at the other end, before another Hartley free-kick found the safe hands of Waterreus, although this time the keeper didn't have to move as much.
Prso was playing really well at this point and he forced a magnificent save from Gordon. Buffel appeared to be held back when the ball broke loose but referee Charlie Richmond waved aside his claims for a penalty.
Prso, Novo and Buffel continued to threaten before Marvin Andrews headed narrowly wide of Gordon's left-hand post after 37 minutes.
Five minutes later however Andrews re-directed Buffel's shot from the edge of the area goalwards, leaving Gordon helpless and Hearts two goals adrift.
The second half was a fairly dull affair but Rangers almost increased their lead after 65 minutes, when a brilliant passing move involving Prso and Shota Arveladze culminated in Buffel firing against the crossbar.
On 81 minutes Ibrox was silenced when Hearts pulled a goal back. Michael Stewart's free-kick fell into a dangerous area and Andrews turned the ball past his own keeper while attempting to clear.
It was a nervy finish for Rangers, but Alex McLeish's side held on for an essential victory.