Suso had another attempt saved on the line by goalkeeper Paul Gallacher, but Steven Thomson fired an equaliser against the run of play before half time.
Hearts made two changes, Lee Wallace and Ruben Palazuelos returned to fitness and took the starting places from Marius Zaliukas and Ian Black. Hearts appeared to have benefited from the changes as they went close to opening the scoring after two minutes.
A Craig Thomson corner found David Witteveen, but the striker's header was hooked off the line by Steven Thomson. David Obua tried his luck from long range, but the midfielder's powerful drive from just outside the box flashed just past the goalkeeper Paul Gallacher's left-hand post.
Hearts took a deserved lead after 31 minutes following a sustained spell of pressure. Suso's fine snap-shot from the edge of the box was turned over the crossbar by Gallacher and, from the resulting corner, Potter cleared Obua's header off the goal-line.
However, it was third time lucky for the Edinburgh side from the next Craig Thomson corner as Goncalves threw himself at the ball to head past Gallacher.
Straight from the restart, Hearts should have gone two ahead when Suso rounded the goalkeeper but delayed his shot long enough for Mair to block and Gallacher pawed the deflected effort off the line.
St Mirren levelled against the run of play after 38 minutes when Steven McGinn's cross was miss-kicked by Dorman, but the ball fell kindly for Thomson, who was clinical with his low drive into the corner of the net from 12 yards.
Witteveen twice came close to restoring Hearts' lead, his clever back-heel following a low Andy Driver cross going invitingly across the face of goal and then the striker headed a couple of feet wide from 15 yards.
The Buddies took the lead when a Billy Mehmet header fell to Dargo 18 yards from goal and his strike partner volleyed into the far top corner of the net.
Witteveen was carried off on a stretcher on 74 minutes after a clattering challenge by Innes.
A disappointed Csaba Laszlo rued "I think we dominated the whole game and had enough chances to win five games.
"Maybe in the second half, we had 20 minutes when we were not so aggressive on the ball.
"I don't like to criticise my players, but sometimes a player comes from another country and does not like to do the simple things. "But, if Suso scores instead of trying to dribble too much, we go 2-0 up and would have an easy afternoon, but then the opponents score when they have had no chances from our mistake."