David Perron scored 3:14 into overtime as the Blues snuck past the Jets 5-4 in Winnipeg.
Tyler Bozak lit the lamp twice in regulation for St. Louis, which won its seventh straight.
Jaden Schwartz logged three assists in the win. Kyle Connor found the back of the net twice as the Jets lost their second in a row.
Blake Wheeler scored the game-tying goal in the third to send it into extra time in defeat.
