The Blues have won eight of nine and improved to 7-1-1 against the Coyotes since the start of the 2011-2012 season.
Phoenix lost its season-high fourth consecutive game.
Oshie recorded his second two-goal game in the last six contests since he was named to the U.S. Olympic team.
Halak improved to 19-6-3 with his second successive win after missing five games due to illnesses. He robbed David Moss from close range with a stick save early in the third period.
Oliver Ekman-Larsson scored for Phoenix, which has been outscored 16-6 during the four-game skid.
Oshie, who has 10 goals, ripped a shot behind Mike Smith midway through the first period off a back pass from Alex Pietrangelo. Oshie scored on the power play in the second period. Jaden Schwartz provided a screen on Oshie's shot from just inside the blue line.
Ekman-Larsson scored a power play goal on a high wrist shot with 48 seconds left in the second period. The Blues had killed their previous 21 penalties.
Phoenix RW Radim Vrbata hit the crossbar with 4:16 remaining the game.
St. Louis, which has won its last five home games, has a plus-61 goal differential, the best in the NHL.
Notes: St. Louis D Roman Polak returned after missing 10 games with a fractured ankle. ... Phoenix C Mike Ribeiro left Monday's contest against Winnipeg with a lower body injury but returned on Tuesday. ...The Coyotes remain the only team in the NHL without a short-handed goal this season. ...St. Louis public address announcer Tom Calhoun worked his 1,200 consecutive home game. ... Blues LW Vladimir Sobotka, who has seven goals and 24 points, missed the game with a fever. ...St. Louis C Patrik Berglund played in his 400th NHL game. ....Phoenix RW Shane Doan is two assists shy of 500.
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