Broberg's one-timer from the high slot at 8:47 off a pass from Robert Thomas came on the Blues' fifth power play of the game.
Broberg also had an assist, and Jimmy Snuggerud scored for a second straight game for the Blues (4-4-1), who had lost their past two games. Joel Hofer made 32 saves.
Cole Perfetti scored for the Jets (4-3-2), who have lost three straight (0-2-1). Stuart Skinner made 27 saves.
Snuggerud put the Blues ahead 1-0 at 12:30 of the first period when Broberg found Dylan Holloway with a seam pass, and Holloway’s centering feed caromed off Snuggerud’s skate in the low slot.
Perfetti tied it 1-1 32 seconds into the third period, one second after a Winnipeg power play expired. Perfetti moved up into the slot from below the goal line to receive a pass from Gabriel Vilardi and score under Hofer’s left pad with a backhand.