The defeat maintains Rangers' 10-point lead at the top of the SPL table, with the Ibrox side having two games in hand.
Georgios Samaras and midfielder Ki Sung-Yueng came in for Marc-Antoine Fortune and Marc Crosas, while St Mirren were without Celtic's on-loan defender Graham Carey.
Higdon was dropped to the Buddies' bench as Steven Robb, Dorman and Craig Dargo came in.
It was almost 15 minutes before the first major action of the match when Mehmet put Celtic keeper Lukasz Zaluska to the test from close range, then Samaras fired towards goal at the other end, but Buddies keeper Paul Gallacher was up to the task when the ball came off the woodwork.
Minutes later, Aiden McGeady threaded through to Robbie Keane who fired for goal, but Gallacher was at full-stretch to prevent the Irishman from scoring.
Paul McGowan's shot was blocked shortly after the half-hour mark, prompting Dargo to speed away on the break, but Josh Thompson kept a cool head and managed to break up the attack.
St Mirren opened the scoring iagainst the run of play when Mehmet took advantage of some careless Josh Thompson defending and flicked on for Dorman to blast in a close-range shot.
Samaras' long-range effort on the stroke of half-time was pushed wide by Gallacher as the hosts went in with the interval advantage.
Immediately after the break the St Mirren fans were claiming for a penalty after the big Greek striker appeared to handle the ball from a Dorman corner, but referee Charlie Richmond was in a poor position and waved for play to continue.
Moments later, McGeady sent a defence splitting pass through to Keane, but the striker was a yard off the pace and the chance to equalise was lost.
Celtic were torn apart at the back for St Mirren's second when Dargo and Mehmet worked a fine one-two on the edge of the penalty area and Thomson slotted past a hapless Zaluska to put the Buddies two up on 58 minutes.
Mehmet almost added a third from a corner, but Zaluska managed to parry wide.
Dorman added his second of the night with six minutes remaining with a fine strike from deep inside the Celtic penalty area.
As the minutes ticked out, Higdon latched on to a free-kick and found Thomson unmarked on the right, and the former Brighton man blasted in to banish the nightmare of Sunday's Co-Operative Insurance Cup defeat at Hampden Park.
90:00+1:02 Rory Loy delivers a pass corner to short, save by Lukasz Zaluska.
89:59 Substitution Stephen O'Donnell is brought on as a substitute for Andy Dorman.
89:09 Substitution Rory Loy is brought on as a substitute for Craig Dargo.
88:48 Mark Wilson delivers the ball.
86:44 Assist on the goal came from Michael Higdon.
86:44 GOAL - Steven Thomson:St Mirren 4 - 0 Celtic Steven Thomson fires in a goal from inside the box to the bottom right corner of the goal. St Mirren 4-0 Celtic.
85:47 John Potter takes the free kick.
85:47 Substitution Michael Higdon replaces Billy Mehmet.
85:47 Foul by Landry N'Guemo on Billy Mehmet, free kick awarded.
85:12 Craig Dargo takes a shot. Save by Lukasz Zaluska.
83:16 Steven Thomson provided the assist for the goal.
83:16 GOAL - Andy Dorman:St Mirren 3 - 0 Celtic Goal scored by Andy Dorman from deep inside the penalty box to the bottom left corner of the goal. St Mirren 3-0 Celtic.
82:33 Free kick awarded for an unfair challenge on Billy Mehmet by Marc-Antoine Fortune. Direct free kick taken by Lee Mair.
80:56 Mark Wilson delivers the ball, Headed effort from inside the area by Robbie Keane misses to the left of the target.
78:18 Free kick awarded for a foul by John Potter on Robbie Keane. Darren O'Dea delivers the ball from the free kick right-footed from left channel.
76:44 Darren O'Dea challenges Billy Mehmet unfairly and gives away a free kick. Jack Ross restarts play with the free kick.
76:38 The ball is delivered by Mark Wilson, save by Paul Gallacher.
74:54 Substitution Morten Rasmussen comes on in place of Edson Braafheid.
74:04 Garry Brady produces a cross, save by Lukasz Zaluska.
73:47 Edson Braafheid gives away a free kick for an unfair challenge on Steven Thomson. Jack Ross takes the direct free kick.
72:29 Mark Wilson produces a cross.
72:09 Unfair challenge on Darren O'Dea by Billy Mehmet results in a free kick. Direct free kick taken by Darren O'Dea.
70:13 Inswinging corner taken right-footed by Andy Dorman from the right by-line, Georgios Samaras fouled by Lee Mair, the ref awards a free kick. Free kick taken by Lukasz Zaluska.
Correction - 69:18 Inswinging corner taken right-footed by Andy Dorman played to the near post, Billy Mehmet takes a shot. Lukasz Zaluska makes a save.
69:18 Andy Dorman takes a inswinging corner to the near post, Billy Mehmet takes a shot. Save by Lukasz Zaluska.
68:46 Georgios Samaras is penalised for a handball. Free kick taken by Lee Mair.
68:32 Steven Thomson produces a left-footed shot from just outside the penalty area that goes harmlessly over the target.
62:07 Robbie Keane is flagged offside by the assistant referee. Indirect free kick taken by Paul Gallacher.
61:25 The ball is crossed by Georgios Samaras.
60:52 Marc-Antoine Fortune crosses the ball.
60:24 Andy Dorman challenges Landry N'Guemo unfairly and gives away a free kick. Direct free kick taken by Landry N'Guemo.
59:30 Substitution Marc-Antoine Fortune on for Sung-Yong Ki.
57:22 Craig Dargo provided the assist for the goal.
57:22 GOAL - Steven Thomson:St Mirren 2 - 0 Celtic Steven Thomson gets on the score sheet with a goal from just inside the penalty area to the bottom left corner of the goal. St Mirren 2-0 Celtic.
57:00 Aiden McGeady delivers the ball.
Correction - 55:32 The ball is sent over by Paul McGowan. Edson Braafheid takes the inswinging corner, Robbie Keane takes a shot. Hugh Murray gets a block in. Inswinging corner taken from the left by-line by Sung-Yong Ki.
55:32 Paul McGowan crosses the ball. Corner taken left-footed by Edson Braafheid from the right by-line, Robbie Keane takes a shot. Blocked by Jack Ross. Sung-Yong Ki takes a inswinging corner.
55:00 Free kick awarded for a foul by Craig Dargo on Landry N'Guemo. Landry N'Guemo takes the free kick.
53:38 Free kick awarded for a foul by Steven Robb on Aiden McGeady. Edson Braafheid crosses the ball in from the free kick, save by Paul Gallacher.
53:19 Free kick awarded for an unfair challenge on Robbie Keane by John Potter. Direct free kick taken by Robbie Keane.
52:37 The referee blows for offside against Billy Mehmet. Lukasz Zaluska takes the free kick.
52:21 Landry N'Guemo gives away a free kick for an unfair challenge on Billy Mehmet. Direct free kick taken by John Potter.
51:35 Craig Dargo crosses the ball, Billy Mehmet takes has a header from just inside the penalty box which clears the crossbar.
51:04 The ball is swung over by Aiden McGeady.
49:53 The ball is delivered by Aiden McGeady, save made by Paul Gallacher.
49:41 The ball is sent over by Paul McGowan, clearance made by Garry Brady.
49:21 The ball is sent over by Mark Wilson, blocked by Steven Robb.
48:56 Landry N'Guemo produces a cross.
47:45 Free kick awarded for a foul by Lee Mair on Georgios Samaras. The free kick is delivered right-footed by Sung-Yong Ki from left channel, Hugh Murray makes a clearance.
47:06 Garry Brady delivers the ball, Effort on goal by Andy Dorman from deep inside the penalty area misses to the right of the target.
46:35 Inswinging corner taken right-footed by Andy Dorman from the left by-line, Georgios Samaras makes a clearance.
46:28 The ball is crossed by Craig Dargo, clearance made by Edson Braafheid.
45:20 Georgios Samaras concedes a free kick for a foul on Jack Ross. Paul Gallacher restarts play with the free kick.
45:01 The referee gets the second half underway.
Half Time
45:00+1:44 It is the end of the first-half.
45:00+1:26 Georgios Samaras takes a shot. Save by Paul Gallacher.
44:03 Billy Mehmet challenges Edson Braafheid unfairly and gives away a free kick. Edson Braafheid restarts play with the free kick.
43:27 Darren O'Dea crosses the ball.
43:20 Edson Braafheid sends in a cross.
41:32 Centre by Aiden McGeady.
39:47 Sung-Yong Ki challenges Hugh Murray unfairly and gives away a free kick. Free kick crossed by Steven Robb.
38:45 Corner taken by Sung-Yong Ki, Georgios Samaras has a headed effort at goal from deep inside the area missing to the right of the goal.
37:37 GOAL - Andy Dorman:St Mirren 1 - 0 Celtic Andy Dorman finds the back of the net with a goal from just outside the area to the bottom left corner of the goal. St Mirren 1-0 Celtic.
36:59 A cross is delivered by Hugh Murray. Jack Ross delivers the ball, clearance made by Josh Thompson.
35:47 Paul McGowan takes a shot. Garry Brady gets a block in.
35:25 Craig Dargo crosses the ball, Darren O'Dea makes a clearance.
33:18 The ball is delivered by Mark Wilson.
32:34 The referee blows for offside. Indirect free kick taken by Lukasz Zaluska.
31:02 Free kick awarded for an unfair challenge on Georgios Samaras by Garry Brady. Landry N'Guemo takes the direct free kick.
30:13 Edson Braafheid fouled by Billy Mehmet, the ref awards a free kick. Darren O'Dea restarts play with the free kick.
28:12 The assistant referee flags for offside against Craig Dargo. Lukasz Zaluska takes the free kick.
27:38 Unfair challenge on Steven Thomson by Edson Braafheid results in a free kick. Jack Ross restarts play with the free kick.
26:57 The ball is delivered by Craig Dargo.
26:31 Georgios Samaras takes a shot. Paul Gallacher makes a comfortable save.
24:19 Inswinging corner taken by Sung-Yong Ki from the left by-line, Hugh Murray makes a clearance.
24:07 Robbie Keane takes a shot. Paul Gallacher makes a save.
20:15 Foul by Hugh Murray on Sung-Yong Ki, free kick awarded. Sung-Yong Ki delivers the ball from the free kick right-footed from right wing, Jack Ross manages to make a clearance.
19:34 The assistant referee signals for offside against Billy Mehmet. Darren O'Dea restarts play with the free kick.
Correction - 15:22 Foul by Lee Mair on Robbie Keane, free kick awarded. Strike on goal comes in from Sung-Yong Ki from the free kick.
15:22 Lee Mair concedes a free kick for a foul on Robbie Keane. Sung-Yong Ki shoots direct from the free kick.
13:35 Billy Mehmet is caught offside. Free kick taken by Darren O'Dea.
13:13 A cross is delivered by Mark Wilson, Shot by Georgios Samaras from inside the area bounces off the post.
12:25 The ball is sent over by Jack Ross, Billy Mehmet takes a shot. Comfortable save by Lukasz Zaluska.
9:00 The ball is crossed by Aiden McGeady.
8:45 A cross is delivered by Aiden McGeady, clearance by Lee Mair.
6:01 John Potter fouled by Robbie Keane, the ref awards a free kick. Paul Gallacher takes the direct free kick.
5:14 The referee blows for offside against Steven Thomson. Indirect free kick taken by Lukasz Zaluska.
4:02 The ball is crossed by Aiden McGeady, clearance made by Lee Mair.
2:49 Free kick taken by Steven Robb.
2:49 Booking Josh Thompson receives a caution for unsporting behaviour.
2:40 Andy Dorman fouled by Josh Thompson, the ref awards a free kick.
2:25 The ball is delivered by Mark Wilson, Hugh Murray manages to make a clearance.
1:43 Sung-Yong Ki gives away a free kick for an unfair challenge on Steven Robb. Paul Gallacher takes the free kick.
0:00 The ref blows the whistle to start the match.
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