Robbie Muirhead opened the scoring for Killie in the second half, but Adam Drury’s leveller gave the Saints some hope of a first point this season until Connolly pounced in the 82nd minute.
The hosts had an early sight of goal when Rory McKenzie’s shot was blocked and they continued to search for an opener, with Josh Magennis sending a header wide.
But John McGinn gave a glimpse of St Mirren’s attacking threat when his drive tested Craig Samson, although Killie went close again as Temitope Obadeyi’s shot was kept out by Mario Kello.
There was further frustration for the home side in the second half as Jamie Hamill blazed over, but Saints were equally wasteful when Kenny McLean fired over the bar.
Substitute Muirhead, however, made no mistake in the 63rd minute when he cut inside and lashed the ball past Kello, but the home side’s joy was shortlived as Drury (71) prodded in McGinn’s low cross at the back post.
But Saints were denied a share of the points when Connolly nodded in a free-kick from Sammy Clingan.