The home side looked to be coasting after a Jamie Mole strike with Saints already short-handed, but Billy Mehmet scored a late equaliser.
Michael Stewart slotted in what proved to be the winner from the penalty spot with 16 minutes left but then missed a second penalty in injury time.
Hearts handed debuts to Slovakian goalkeeper Marian Kello and to Ugandan midfielder David Obua.
Lee Wallace had an early chance when he was played in by Mole, but Mark Howard pulled off a wonderful save to push the ball for a corner.
Mole then had a chance himself after a great pass from Stewart but Will Haining managed to block his effort.
It was all Hearts in the opening stages and Stewart then sent Andy Driver clear but his shot finished narrowly wide.
Laryea Kingston then tried his luck with a superb strike from 25 yards which Howard did well to tip over his crossbar.
There was a scare for Hearts when Stewart was short with a headed back pass, but Christophe Berra came to his rescue to beat Mehmet to the ball.
But St Mirren were reduced to ten men after 26 minutes when Antonio Tonet, booked for a foul on Jason Thomson just three minutes earlier, picked up a second yellow card for a challenge on Stewart.
It gave Hearts the encouragement they needed and they scored shortly before half-time.
Stewart fed Mole and he fired the ball into the roof of the net from 20 yards with Howard only able to help the ball into the goal.
Four minutes into the second half, Driver was denied by another great save from Howard as Hearts sought to kill the game off.
Substitute Deividas Cesnauskis then looked set to score, but Jack Ross managed to scramble the ball past for a corner.
There was a scare for Hearts midway through the half when Mehmet set up Jim Hamilton, but the striker's shot was blocked by Obua.
Hearts did not heed the warning and Mehmet stabbed the ball home from close range after the home side had failed to defend a Franco Miranda free-kick and Hugh Murray fired the ball across goal.
Driver thought he had put Hearts back in front two minutes later, but Howard pushed his shot over the crossbar.
Moments later, Driver was fouled in the box by Miranda and Stewart made an expert job with the spot-kick.
In injury-time, Ross fouled Audrius Ksanavicius in the area, but this time Stewart's shot was brilliantly turned away by Howard.