Stevenson struck in the 32nd minute following a counter-attack and Sutton ensured Hearts moved into 10th place in the Clydesdale Bank Premier League, six points behind sixth-placed Hibernian with three games left until the split.
Hearts could have had more, with Michael Ngoo alone having more than half a dozen decent chances, while St Johnstone also created a number of opportunities, especially in a frantic first half. Both sides had goals disallowed.


