Clyde had a goalscoring opportunity inside the opening minute but Roddy Hunter's shot lacked power and Bryn Halliwell made an easy save.
The game went through a touchy patch with Saints pair Paul Lawson and Martin Hardie picking up yellow cards.
Chances were at a premium and Saints' only effort on goal during the opening 45 minutes was a Hardie header from Paul Sheerin's cross, which went straight into the arms of David Hutton.
Clyde threatened danger from a Michael McGowan cross but Simon Mensing produced a vital clearing header in the middle of the Saints defence.
The away side went down to ten men in the 43rd minute when Lawson was red carded for elbowing Chris Higgins as the players jostled while waiting for the delivery of a corner.
Jason Scotland had a golden opportunity to put Saints in front. Put clean through by Goran Stanic he looked at least two yards offside, but justice was done when he dwelt too long on the ball and keeper Hutton scooped it off his toes.
Clyde skipper Stephen O'Donnell fired one over the bar from outside the box before Imrie's late strike settled the issue.