The former Inverness striker hooked home a 67th-minute equaliser and his cross soon led to Billy Mehmet's eighth goal of the season.
Substitute Tom Brighton then killed off Falkirk, who had taken the lead in the 55th minute when Brian McLean made sure Alex MacDonald's header crossed the line.
The only downside for the Paisley club was a shoulder injury for Dargo, who netted the winner against Hearts in their previous game.
Falkirk manager Eddie May suffered another blow as he continues to await his first SPL victory as striker Carl Finnigan was stretchered off.
May was already without Icelandic striker Kjartan Finnbogason, who has been struggling with a back injury and joined Thomas Scobbie on the sidelines after the defender began a six-week lay-off with pelvic problems.
An unchanged St Mirren kept their hosts hemmed in for much of the opening quarter. Saints were causing Falkirk problems with some measured build-up play down the right and Craig Dargo headed straight at Olejnik from a Jack Ross cross.
Dargo had another chance after John Potter flicked on Andy Dorman's corner, but Jackie McNamara got a crucial touch before the Saints striker headed at Olejnik from close range.
Ryan Flynn had a volley comfortably held from a tight angle at the other end and Falkirk began to improve after the right winger swapped places with Danijel Marceta, who had started in a central role.
Vitor Lima and Marceta both shot just over from 25 yards after some sharp passing and a more direct approach almost paid dividends when Potter misjudged Twaddle's long ball. However, Paul Gallacher was fully behind Finnigan's volley from 15 yards.
Finnigan was replaced by Mark Stewart after tangling with Hugh Murray, earlier booked for a foul on Flynn, as the players contested a loose ball.
St Mirren were awarded the free-kick and eventually worked the ball out to Ross, whose powerful 25-yard drive was well held by the diving Olejnik.
Scott Arfield, who has been troubled by an ankle injury recently, was replaced by MacDonald in the 54th minute and the on-loan Burnley forward was celebrating within 60 seconds.
The substitute headed Twaddle's deep corner off the underside of the bar and Ross failed to clear before McLean nudged the ball into the back of the net.
MacDonald claimed the goal - Falkirk's first in six games - but the defender may have got the crucial touch.
St Mirren, with Allan Johnston on, pushed forward and Dargo netted from a tight angle despite Olejnik's attempts to save after Dorman and Stephen McGinn had worked a short corner towards the back post.
Dargo turned provider as Saints took the lead four minutes later. The striker did well to cross from the right wing and, although Olejnik saved brilliantly from Dorman's header, Mehmet turned home the rebound from six yards.
Dargo injured his shoulder as he fell following the cross and was instantly replaced by Tom Brighton.
Falkirk's comeback attempts lacked conviction and Brighton made sure of the victory in the 86th minute with his first St Mirren goal.
Olejnik could only palm the ball into the path of Brighton as he and Jackie McNamara both tried to clear Dorman's driven cross, and the former Millwall striker lashed it into the roof of the net.