Karel Vejmelka stopped 40 shots, Travis Boyd had two goals and an assist in the third period, and the Coyotes beat the Blues 6-2 on Tuesday night.
The Coyotes got off to a shaky start, giving up a breakaway for the first of Pavel Buchnevich's two goals, but Vejmelka kept them in it with a series of spectacular saves.
Christian Fischer and Nick Schmaltz scored to give Arizona a 2-1 lead and Boyd put it away with his two third-period goals. Clayton Keller added a goal and two assists, and Lawson Crouse also scored to give the Coyotes 16 goals in three games against St. Louis this season.
St. Louis didn't give its goalie much of a chance and had a hard time scoring in any situation. Jordan Binnington gave up six goals on 27 shots for St. Louis, which has lost eight of nine.
The Coyotes gave up 15 combined goals in their previous three games and found themselves in another hole against the Blues.
Arizona had two early icing calls during long shifts in its own end and Buchnevich took advantage of a breakaway, beating Vejmelka to the glove side for his 10th point in six games.
The Coyotes snapped out of it and scored midway through the first period when a pass by Connor Mackey caromed hard off the backboards to the other side of the goal. Fischer easily put it into an empty net with Binnington out of position.
Arizona had more defensive breakdowns to start the second period, giving up a couple of breakaways. Vejmelka stuffed both, blocking Brandon Saad, then making a spectacular glove save on Robert Thomas on the 2-on-0.
Buchnevich scored midway through the third period, lifting a backhander over Vejmelka's stick shoulder. Boyd pushed the lead back to two goals by punching in a rebound for his first multi-goal game and 100th career point.
St. Louis hosts San Jose on Thursday.