Midway through the first half, a forward ball from Barry Robson was met by Adam Rooney, who then proceeded to head it towards Pawlett, but Danny Wilson managed to usher it out for a corner, which came to nothing.
Hearts stepped it up a gear in the early stages of second half, with a quick free kick releasing David Smith, who then proceeded to skip past his man and attempt a shot, but he fired over.
The Jambos made things difficult for themselves when Wilson was sent off midway through the second half, with the away side scoring a goal just a few minutes later courtesy of Willo Flood's free kick.
Hearts, however, won a penalty with just three minutes left to play when Logan fouled Paterson in the box. Hamill stepped up and sent the ball down the middle for the equalising goal.
A frantic final period ensued, but the game eventually finished 1-1, which means that the Jambos are still not mathematically relegated.