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Daniel Grainger scored the game's only goal with a strike from outside the penalty box, in front of a sell-out crowd at Tynecastle. The victory moves Hearts up three places to seventh.
Bottom-of-the-table Dundee found some form in front of goal in their game against Hibernian. The 3-1 win was the home side's third win of the season, and moves them to within a point of 11th-placed St Mirren.
Results in full: Aberdeen 0-2 Celtic, Dundee 3-1 Hibernian, Hearts 1-0 St Mirren, St Johnstone 1-1 Ross County.