Scott Arfield gave the hosts the lead seconds before the break from the penalty spot after Chris Innes was sent off for a head-butt on Brian McLean.
The Bairns had looked comfortable in the second period but O'Donnell pounced just moments after goalkeeper Robert Olejnik parried Craig Dargo's shot to nod home Graham Carey's cross as the Buddies moved four points clear at the bottom.
After a slow start, the visitors settled into proceedings and O'Donnell had an ambitious shot from the right which flew over the bar.
Andy Dorman then passed up a great chance to put his side ahead when he headed Graham Carey's cross into the ground and wide from eight yards.
After surviving a period of sustained pressure, Falkirk then strung together a neat move which culminated in Pedro Moutinho blasting a half volley just over.
Despite the importance of the game, it was surprisingly open as Dorman nodded another header wide from a Carey cross in the 21st minute.
The latter part of the first half failed to live up to the opening of the game as both sides struggled to conjure up any opportunities.
Buddies midfielder Carey unleashed an ambitious 35-yard free-kick which bounced straight into Olejnik's hands.
The half then finished in controversy after Innes was sent off for an apparent head-butt on McLean and referee Willie Collum awarded a penalty.
Scott Arfield stepped up and rolled the penalty into the right-hand corner, sending the goalkeeper the wrong way.
St Mirren manager Gus MacPherson opted against making any half-time substitutions despite going down to 10 men, although O'Donnell dropped back to defence to help his colleagues.
The home side were keen to extend their lead and Moutinho had a left-footed strike deflected clear by the leg of Potter.
Falkirk enjoyed having a numerical advantage as they stroked the ball around the park comfortably. After patient build-up Mark Stewart sliced an effort wide from 18 yards and then got in behind Steven Robb on the right wing but his cross was cut out.
Falkirk defender Kieran Duffie replaced McLean at right-back and the youngster picked up a yellow card for a tackle on Carey even though he appeared to win the ball.
Bairns manager Steven Pressley made his intentions clear by introducing towering striker Enoch Showunmi for midfielder Colin Healy and MacPherson responded by bringing on marksman Michael Higdon, who scored the priceless goal that kept Falkirk in the top flight last season, for full back Steven Robb.
Billy Mehmet came within inches of equalising in the 69th minute when his shot on the turn from 18 yards just missed the post.
Falkirk captain Darren Barr watched on agonisingly as he had a left-footed shot on the volley from Moutinho's corner cleared off the line in a frantic goalmouth scramble.
St Mirren threw caution to the wind by getting players forward and they were rewarded with five minutes left.
After Olejnik parried Craig Dargo's curling shot, Carey's in-swinging corner was headed to the back post where O'Donnell rose to nod into the goal from just a yard out.