David Perron netted the winner in the fourth 2, at MTS Centre.
To start the final round, Andrew Ladd hit the space between Jaroslav Halak's arm and body. As the Blues netminder slid backwards in his crease, the puck dropped behind him, and only the quick sweeping motion of his pad prevented the disc from moving over the goal line.
Perron followed and beat Chris Mason with a high backhander from the left side.
David Backes and Perron tallied in regulation for the Blues, who have won two in a row and four of six. Halak ended with 39 saves.
Blake Wheeler scored twice for the Jets, who fell to 3-0-2 on their current eight-game homestand. Mason made 14 stops.