Stephen McGinn thought he had grabbed the winner for Saints but there was plenty of drama to come when Kevin Kyle's late leveller for the home side looked set to force the tie into extra-time.
However, it was Dorman - who came off the bench after an hour - who had the final say when he claimed the decisive goal in stoppage-time as Killie suffered an agonising defeat.
St Mirren wasted no time in trying to gain an early advantage when Billy Mehmet went to ground under pressure from Ryan O'Leary with less than a minute on the clock but referee Dougie McDonald ignored the pleas for a penalty.
At the other end, Paul Gallacher was called into action to pull off a decent save when Jamie Hamill picked out Kyle at the back post but the offside flag was raised anyway.
The Saints goalkeeper then produced an impressive double block, firstly to deny Kyle and then to prevent Conor Sammon's close-range follow-up effort from finding the back of the net.
Killie continued to press for the opener and were denied by the woodwork when Kyle threw himself in front of a Garry Hay free-kick only to see his header crash off the post.
Referees had dominated the headlines following the SPL action at the weekend and the match official had another call to make when Garry Brady beat several players before bursting through on goal.
His run was ended when Steven Old appeared to handle in the box but, surprisingly, there was a lack of claims from the visitors and McDonald signalled for play to continue.
The first half had been free of bookings but Manuel Pascali - who was harshly sent off against Rangers at the weekend - earned the first caution of the match four minutes after the restart, before being replaced by David Fernandez five minutes later.
Killie goalkeeper Mark Brown stood tall to block an angled drive from Steven Thomson after John Potter had teed up the shot.
But he was picking the ball out of the back of the net with 64 minutes gone when McGinn collected the ball on the edge of the box and rifled high into the net to hand Saints the advantage.
Fernandez should have restored parity when he exchanged a one-two with Sammon before unleashing a ferocious shot from just inside the box but, unfortunately for the home side, his effort whistled narrowly past Gallacher's left-hand post.
Hamill then went to ground after jostling with Lee Mair in the box in a desperate late bid to salvage something from the tie but, once again, McDonald was unimpressed.
Instead, Hamill brushed himself off and delivered the cross for Kyle to direct a header past Gallacher with just three minutes remaining to keep Kilmarnock's hopes alive.
However, the Ayrshire outfit were dealt a cruel blow when Dorman raced on to a Thomson ball to slot past Brown for the Buddies' dramatic late winner.