Hamilton struggled to create chances despite dominating possession against 10-man Saints, until Antoine-Curier headed home Dougie Imrie's cross with 15 minutes left.
St Mirren had Jure Travner sent off in the 25th minute after Hugh Murray had been stretchered off on his record-breaking appearance, and they failed to capitalise after Hamilton skipper Alex Neil was dismissed following the goal.
Victory would have secured St Mirren's safety for a fifth consecutive season and they remain six points and 10 goals better off than the bottom club, but Accies at the very least have taken the fight another week and avoided the ignominy of seeing their rivals celebrate.
A bleak day for the hosts started badly when Murray, who broke his former manager Tony Fitzpatrick's club record as he made his 459th appearance, was carried off after twisting his knee while sliding in on Jim McAlister before the five-minute mark. Kenny McLean came on.
The visitors dominated possession even before their numerical advantage and Imrie came close with a 30-yard strike. David Buchanan sliced a Travner cross just over his own goal but Hamilton were soon back in control.
And their grip in the game tightened when Craig Thomson handed Travner a second - and unavoidable - yellow card for a late tackle on Imrie 10 minutes after the left-back had been booked for pulling back Nigel Hasselbaink.
Imrie came close again from long range before Hamilton almost shot themselves in the foot when Mensing gifted Michael Higdon the ball, but Tomas Cerny held the striker's effort from 25 yards.
St Mirren kept both Higdon and Craig Dargo up front, moving McLean to left-back, but Accies were unable to exploit their man advantage before the break, with Ali Crawford and Hasselbaink both ending long spells of possession with wayward strikes.
Accies created the chance of the half in injury-time when Imrie robbed Lee Mair of possession and crossed perfectly for Hasselbaink, but the Dutch striker headed straight at Paul Gallacher from close range and the goalkeeper blocked with his legs.
St Mirren manager Danny Lennon moved to a 3-5-1 at half-time with defender John Potter replacing Dargo.
Hamilton hit the bar four minutes into the second half - but only from a mis-hit Buchanan cross - and the pattern of the game remained unchanged with Accies failing to find an end product to their possession.
Visibly frustrated manager Billy Reid made two changes around the hour mark with Antoine-Curier coming on to join Imrie up front and James Chambers playing just off them. Mark Carrington and Hasselbaink made way.
Steven Thomson ran through to fire a shot that Cerny pushed over, moments before the midfielder went down theatrically following an innocuous foul by Neil, who had been booked for a poor and needless challenge on the same player just before the break. But the referee resisted demands to even the numbers.
Saints threatened again on the break and Higdon squared to McLean, but he stabbed wide under pressure. Reid brought on striker Tom Elliott for Buchanan as the game entered the final 20 minutes.
Hamilton were struggling to put the St Mirren defence under pressure until Imrie crossed from the left and Antoine-Curier rose at the near post to power a header into the roof of the net.
Chambers soon set up McDonald, whose effort was blocked, and the goalscorer, whose shot was pushed just wide of the far post by Gallacher.
But the game took another twist when Neil received his second yellow card in the 80th minute when he bundled over St Mirren substitute Gareth Wardlaw.
However, Wardlaw volleyed over following a long ball in injury-time as Hamilton held on.
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