Michael Schjonning-Larsen scored the only goal as Hearts boss Derek McInnes lost on his return to Rugby Park, where he enjoyed three years as Kilmarnock boss.
No side outside of Celtic and Rangers has won the Scottish title for 41 years.
Hearts have led for virtually the entire campaign, but a series of injuries to key players caught up with the Jambos in a poor performance.
Should Rangers win at St. Mirren on Sunday, the top three would be separated by just three points with eight games remaining.
Celtic boosted their title defence by coming from behind to beat fourth-placed Motherwell 3-1.
Motherwell has been on the fringes of the title race themselves prior to last weekend's defeat at Dundee and dominated Celtic when the sides last met in December.
The visitors were on course for back-to-back wins over the Scottish champions when Elijah Just fired in after Reo Hatate had been robbed at the edge of his own box on 32 minutes.
However, the roles were reversed just six minutes later when Celtic this time won possession inside the Motherwell box and Yang Hyun-jun slotted in an equaliser.
The decisive moment came 19 minutes from time when Emmanuel Longelo pulled down Daizen Maeda from a corner.
A VAR intervention saw a penalty awarded and a red card shown to Longelo.
Tomas Cvancara, who scored the winning penalty to beat Rangers in a bad-tempeted Old Firm showdown last weekend, coolly converted from the spot.
Yang then raced through to fire home his second of the afternoon and seal a vital three points for Martin O'Neill's men.