Hearts had taken the lead through Icelandic international Eggert Jonsson in the 77th minute but the Buddies, playing their second game in two days, earned a share of the spoils at the death.
The unmarked Dorman poked the ball past Janos Balogh at the back post from Jack Ross's free-kick.
If St Mirren were weary following Thursday's Scottish Cup win over Motherwell, they did not show it after finishing the game the stronger of the two sides.
After a tame start, the game came to life in the 18th minute with a flurry of action at both ends of the pitch.
St Mirren mustered a chance when Jim Hamilton edged in front of Robbie Neilson to meet Dorman's free-kick but his header just missed the target.
Seconds later, Hearts striker Christian Nade had a shot from 18 yards that was parried by Chris Smith and the visitors conceded a corner.
From Andy Driver's delivery, debutant Mo Camara cleared Jonsson's effort off the line before Nade blasted the loose ball wide.
Bruno Aguiar then volleyed wide from the edge of the area with the St Mirren defence failing to clear their lines.
Hearts registered another effort at goal in the 33rd minute when David Obua rose highest to connect with Aguiar's corner but Smith easily collected the ball.
Obua then cut in from the left past Camara and unleashed a 20-yard shot that Smith got down well to save.
St Mirren midfielder Hugh Murray became the first player to be booked after he blatantly obstructed Lee Wallace as the left-back darted forward.
As Aguiar waited to take the free-kick, Scott Cuthbert and Nade were also booked for an off-the-ball tussle.
From the set-piece, Aguiar's curling effort clipped the crossbar with Smith scrambling across his goal.
Hearts made a change at the interval with Laryea Kingston replacing Gary Glen, who had taken a blow to the head in the first half.
However, Kingston's participation lasted just six minutes as he was stretchered off after appearing to pick up a knee injury, and the Ghanian international was replaced by Ruben Palazuelos.
The Hearts supporters grew restless over the lack of goalmouth action as St Mirren defended stoutly in the face of pressure from the hosts.
St Mirren were still very much in the game, however, and Jonsson was called upon to deflect Stephen McGinn's shot wide.
Hearts welcomed back Saulius Mikoliunas from injury when the Lithuanian replaced Michael Stewart.
The winger had been sidelined since Hearts beat St Mirren in November after sustaining a knee injury.
And, within seconds of his arrival, Hearts broke the deadlock in the 77th minute.
Jonsson kept Neilson's free-kick to the back post in play and, after Obua's shot hit a ruck of bodies in the six-yard box, Jonsson slammed the rebound into the net.
Mikoliunas then shot wide from 25-yards as Hearts looked to put the game beyond doubt.
Five minutes from the end, substitute Craig Dargo wasted a good chance to equalise after he headed Camara's cross over the bar from close range.
Mikoliunas then swung wildly and missed the target right in front of goal after Obua crossed from the left.
Hearts were made to rue that missed chance as Dorman slid in to level in injury-time. Ross's free-kick was headed back across goal and the unmarked Dorman placed the ball under Balogh from close range.
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