Dorman netted his fourth goal in as many games after Steven Thomson had given Saints a 77th-minute lead.
Motherwell had enjoyed the majority of possession but they lacked the cutting edge to claim the victory they needed to leapfrog Hibernian.
St Mirren continue to prove a thorn in Motherwell’s side – the Steelmen have now won just two out of 13 games against the Paisley side, who knocked them out of the Homecoming Scottish Cup in February.
Motherwell had an unfamiliar look to their side after skipper Stephen Craigan returned after missing two games with a calf injury.
Brian McLean moved to right-back, Paul Quinn to left-back and Stevie Hammell took up a midfield role.
St Mirren were forced into two changes, with captain John Potter suspended and Billy Mehmet injured. Will Haining and former Well striker Jim Hamilton came in.
Saints’ pressing game kept Motherwell inside their own half for much of the first 10 minutes but the home side suddenly burst into life.
David Clarkson’s powerful 20-yard strike was blocked by visiting goalkeeper Mark Howard and the rebound flashed past the onrushing John Sutton, who soon headed just wide from Quinn’s cross.
Hughes and Jim O’Brien were not far away with long-range efforts, the first taking a deflection, and Clarkson almost got on the end of several balls into the box.
The home side could not maintain the pressure and the game entered a scrappy phase as St Mirren hit the ball long for Hamilton more often than not.
O’Brien passed up the chance to shoot first-time after Hammell’s half-cleared corner rolled out to him on the edge of the box, Howard being wise to his attempted chip after the winger had taken a touch.
Graeme Smith rescued the hosts in the final minute as St Mirren created the best chance of the half.
Dorman’s long pass caught out the Motherwell defence and Craig Dargo raced away from Craigan, but Smith came off his line to block the striker’s low shot.
Fir Park was slightly fuller than usual after 6,626 fans took advantage of the £5 admission prices but the atmosphere was tense as the game re-started.
It did not improve much and two long-range efforts were all Motherwell had to show for their early efforts.
Howard comfortably smothered Clarkson’s 20-yard strike before Hughes beat two men to set himself up for a long-range effort, but his left foot sliced the ball well wide.
Sutton twice got his head to O’Brien crosses but Howard caught both efforts.
Motherwell needed inspiration but it was the visitors who made the first change, replacing Hamilton with Dennis Wyness in the 73rd minute.
Haining’s late challenge on O’Brien earned the defender a yellow card and Motherwell a free-kick in a dangerous position, but McLean headed the winger’s whipped delivery over from close range with his back to goal.
Motherwell suffered a body blow when some poor defending allowed Thomson the simple task of netting his first Saints goal.
After another high ball, Dargo lobbed it back over Smith from near the byline and Reynolds’ attempt to clear merely set up Thomson three yards out to tap home.
Jamie Murphy soon replaced Maros Klimpl as home boss Mark McGhee finally gambled but little changed before striker Cillian Sheridan replaced Craigan in the 85th minute.
Any lingering hopes were extinguished in two minutes later when Dorman volleyed home a magnificent 30-yard strike.
The midfielder controlled Dargo’s pass and, despite having a clear run at goal, had the confidence to lob the ball over Smith and just under the crossbar.
Motherwell’s unproductive afternoon was summed up in the final minute when Hughes headed Hammell’s corner against the far post.