Kilmarnock left it late to beat third-placed Motherwell at Fir Park, registering the only win in a cagey day of Scottish Premiership football.
Craig Slater's 90th-minute strike was enough to complete a second-half Killie comeback, after Iain Vigurs had put Well in front before half time.
Second-placed Aberdeen can be thankful for Niall McGinn's second-half strike, which helped the Dons grab a point against in-form Dundee United, who led early on through Paul Paton at Pittodrie.
St Mirren eased their relegation fears when Sean Kelly grabbed an equaliser to hold Inverness Caledonian Thistle to a 2-2 draw. The result means that Hearts edge closer to an inevitable relegation from the Premiership.
Partick Thistle's own survival hopes were boosted by a late Kris Doolan strike away to St Johnstone, cancelling out Stevie May's early goal for the Perthshire outfit.
Results in full: Aberdeen 1-1 Dundee United, Celtic 1-1 Ross County, Inverness CT 2-2 St Mirren, Motherwell 1-2 Kilmarnock, St Johnstone 1-1 Partick Thistle
