Stevenson dents Rangers' title charge
Stevenson's winner lifted the home side to within four points of league leaders Celtic, just two points behind their second-placed opponents.
Walter Smith's side, who missed the chance to go top, were boosted by the return of Madjid Bougherra, Steven Naismith and Sasa Papac and they threatened immediately as Kyle Lafferty's shot was pushed away by Hearts goalkeeper Marian Kello.
Lafferty had another chance for Rangers when he collected from Maurice Edu but his miscued effort was easily gathered by Kello. Rangers still looked dangerous and Jamie Ness's swerving effort was tipped just wide of the far post by the Hearts' goalkeeper, who blocked another stinging shot from Lafferty as Rangers kept pushing for the breakthrough. Kello was then called into action again to deny Steven Naismith the opener from a powerful drive.
With half-time approaching, Hearts could have snatched the lead as Rudi Skacel flashed a shot across the face of goal before Allan McGregor blocked from Stephen Elliott.
Rangers should have broken the deadlock soon after half-time when Papac went on a surging run before seeing his close-range shot blocked by Kello. But, despite all the visitors' pressure, it was Hearts who took the lead in the 77th minute when Skacel's attempt on goal fell to Stevenson who poked the ball home from close-range.
The visitors could have hauled themselves level when substitute Nikica Jelavic tried his luck with an ambitious overhead kick that crashed off the underside of the bar but Hearts were able to hold on for a famous win.