Bryan Little scored for the Jets (14-14-4), who started a little slow but more than held their own in the first period, outshooting the Blues (20-6-3) by an 8-2 margin.
Four of those came during the Jets' one power play late in the period. Winnipeg may have the worst power play in the league, but great saves by Brian Elliott kept the puck out of the St. Louis net.
Alex Steen turned things around in the second with the Blues' first goal.
He was behind the Winnipeg goal-line midway between the net and the boards at 4:44 when he slid a puck behind Ondrej Pavelec that banked off the Winnipeg goalie to put the Blues ahead 1-0.
Pavelec was focusing on those in front of the net rather than the Blues' leading sniper to his right. It was Steen's 21st goal of the season.
Steen's goal helped give the Blues energy and they outshot the Jets 8-5 in the second, although Winnipeg also had to kill a Blake Wheeler interference penalty.
But Little evened things up just three minutes into the third as he won a faceoff and then snapped a pass from linemate Andrew Ladd past Elliott on a power-play, thanks to a tripping call against Vladimir Sobotka.
Winnipeg failed to get a shot off on a second power play in the third and killed another Wheeler minor for slashing. The Jets also failed to score on another power play about 13 minutes in.
Jets defenceman Dustin Byfuglien was sent off with just over three minutes left for hooking, which gave Shattenkirk his chance to score his third goal of the season.
St. Louis was coming off a 5-2 home-ice loss to Anaheim and had lost three of their last four coming to Winnipeg. The Jets hadn't played at home since Nov. 23 but were 4-2 on an Eastern road swing.
Notes: Jets' Mark Stuart left in the third bleeding profusely from the mouth after a goalmouth scramble. ... Wheeler had been on a three-game point streak going into the game. ... The Jets are still the only team in the Central that has managed to beat the Blues this season, 4-3 in a shootout Oct. 18. ... St. Louis went into Tuesday's came with an impressive 9-0-1 record against division opponents.