Early St Mirren pressure spread panic in the Accies defence with Simon Lappin chipping over just before David McEwan pushed a Brian McGinty shot behind after 16 minutes.
It was a time when the visitors needed old heads, and losing veteran Derek Ferguson through injury came as a bitter blow. Chris Aitken replaced him after 21 minutes, but two minutes later the Saints took the lead.
Stewart Kean scored the goal that had been coming, shooting past McEwan low at his near post after Ryan McCay crossed in from the left.
The Saints went close twice more but went in at the break one-nil up.
After the re-start the Accies looked to be slightly better organised, and Corcoran volleyed over from 20 yards.
But the Saints soon took over the match and Kean was unlucky to see a shot deflected behind after 62 minutes.
The home team were becoming more dominant, and after 76 minutes substitute Allan Russell extended their lead. Lappin crossed in from the left for Kean, who knocked the ball back to Russell to fire home from 20 yards.
Three minutes later Lappin was the provider again from the left, and Kean was unmarked to seal an empahtic win from 10 yards.