Dorman struck late on with the only goal of the game in what was a scrappy clash at New St Mirren Park as both sides desperately tried to haul themselves away from the danger zone.
In a further boost for the Paisley club, bottom side Falkirk also suffered defeat against Hamilton, meaning Saints are now four points clear of the drop zone, while Killie remain a single point ahead of rock-bottom Bairns.
St Mirren were dealt a blow ahead of the clash when Billy Mehmet failed to make the squad. The Saints striker picked up a knock in training yesterday and Michael Higdon took his place in the starting line-up.
In contrast, the visitors were boosted by the return of a trio of key players, with Kevin Kyle back from suspension and Frazer Wright and Scott Severin both recovering from injury ahead of the trip to Paisley.
Kilmarnock came close early on when Manuel Pascali rose above everyone else to meet a corner from the right only to bullet his header inches past the post.
At the other end, Saints were threatening when attempts to clear a David Barron ball into the box broke to Stephen O'Donnell and he rifled into the side-netting.
There was concern for the home side when Hugh Murray left the pitch on a stretcher after 22 minutes following a lengthy period of receiving treatment following a collision with Kyle. He was replaced by Garry Brady.
Kyle had a chance to open the scoring when he collected a short pass from Mark Burchill only to see his weak effort trundle wide from eight yards.
Burchill himself passed up a decent opportunity moments later when he directed a header just over from close range as the Ayrshire side pressed for the opener before the break.
Saints almost sneaked a goal instead when Steven Thomson whipped an inviting cross into the box only for Higdon's header to flash narrowly past Cameron Bell's right-hand upright, before the keeper blocked well from Brady.
Severin was then denied by the woodwork deep into the eight minutes of stoppage time when he exchanged a one-two with Jamie Hamill before his ferocious volley smacked off the inside of the post.
Fears over Murray, who was reportedly knocked out cold in the collision, were eased at half-time when the PA announcer informed concerned fans that the veteran midfielder was fine.
Severin and Burchill made way for James Fowler and Chris Maguire as Killie made two changes ahead of the second half.
But it was the home side who could have broken the deadlock when Graham Carey's cross picked out Dorman and he flicked across the face of goal and wide of target.
The match was proving impossible to call and Killie were threatening when Liam Kelly squared for Maguire who stabbed wide from a couple of yards under pressure from Steven Robb.
Kilmarnock fans protested furiously when Maguire went to ground under pressure from Lee Mair in the box but there appeared little in the incident and there was no penalty award from the referee.
The breakthrough finally came after 73 minutes and it was Saints who were celebrating. Carey's corner was met by Higdon and he nodded on for Dorman to send a firm header past the grasp of Bell.
Killie threw bodies forward in search of a leveller and Maguire saw his shot smothered low at the post by Gallacher, before the keeper blocked a Kyle header with seconds to go as Saints held on for a vital win.