Saints replied with some neat attacks and John Sutton had a shot blocked by Grant Munro, a Simon Lappin free-kick raged inches wide and veteran Andy Millen poked a Billy Mehmet cut-back outside a post.
Tony Bullock saved a low drive from Ross Tokely and Mark Brown had to rush out of his goal twice in a minute to thwart darting runs from Lappin.
Barry Wilson should have put the visitors ahead when he fired past as Bullock charged out to rescue his hesitant defenders.
Saints were giving away too much possession and Kevin McGowne's mistake allowed Craig Dargo to bore in on goal but Hugh Murray made a superb tackle to deny a certain goal.
Dargo made up for his missed opportunity when he side-footed the ball past Bullock after Wilson 's cross hit Millen and fell for the striker.
Bold substitutions by manager Gus MacPherson saw Saints throw wave after wave of assaults at Caley's rearguard and Sutton rose to flick a fine header past Brown from Lappin's corner to secure a share of the points.