After a goalless draw which earned both sides a point, the extra point was decided with a shoot out and East Kilbride triumphed 6-5.
St Mirren had a chance to win on penalties after goalkeeper Vaclav Hladky saved Ryan Sinnamon's effort but Danny Mullen blazed his spot-kick over the bar.
Sub Cody Cooke was forced to retake his penalty as referee Colin Steven had not blown his whistle and his second effort was saved by the excellent Alan Martin.
Ruari Paton then stepped up to win the shoot-out and St Mirren now face a tall order to progress from their group, having picked up four points from their opening three games, with just one game remaining.
St Mirren should have taken the lead after 22 minutes when Tony Andreu's flick sent Oan Djorkaeff in on goal.
But the Frenchman, son of World Cup winner Youri, hesitated inside the penalty area when he should have shot and that allowed Sinnamon to get back and make a goal-saving challenge.
St Mirren then enjoyed a period of pressure as they tried to make the breakthrough and captain Stephen McGinn tested goalkeeper Martin with a drive from the edge of the box.
Kyle Magennis then had a chance when he got to a Andreu pass before Martin and went round the goalkeeper but the angle was too tight and he fired into the sidenetting.
Just before the break Martin produced a stunning double save.
Stephen McGinn slid a through ball for Danny Mullen and his first effort was beaten away by Martin and then the Saints striker lashed the rebound goalward but East Kilbride's goalkeeper showed tremendous reactions to keep it out.
St Mirren pushed for the breakthrough after the interval with Djorkaeff, Mullen and Andreu all having efforts on target but Martin was equal to all of them.
Sub Cooke then went close with a header from a Cammy MacPherson cross but his effort just cleared the crossbar.
Martin then produced a brilliant reaction save when sub Jim Kellerman fired a snapshot through a crowded penalty area.
With neither side able to make the breakthrough, both picked up a point and the bonus point was decided from the spot.