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.
Halak improved to 19-6-3 with his second successive win since missing five games due to an illness. The mysterious ailment, diagnosed as a severe flu, sapped his strength and forced him to the sidelines from Dec. 29 to Jan. 7.
''I had a fever that wouldn't go away and I kept getting tired real fast,'' Halak said. ''Now that the virus is gone, I'm feeling pretty good.''
Halak made several impressive stops in the third period to protect a 2-1 lead. He robbed David Moss from close range with a stick save two minutes into the period. He also thwarted Antoine Vermette and Tim Kennedy down the stretch.
''This is a game where the goalie saved us,'' St. Louis coach Ken Hitchcock said. ''He was terrific from start to finish.''
Phoenix outshot St. Louis 8-2 in the third period and dominated play.
''I thought we pushed hard,'' Phoenix coach Dave Tippett said. ''We gave ourselves a chance to get some points.''
But Halak would not budge.
''You've got to give them credit, they came out really hard in the third,'' Halak said. ''I'm glad we got the two points, but we all know we can play better.''
Halak made 33 saves in a 5-0 shutout in Calgary on Thursday. He says he was not 100 percent in that game, but believes he is very close to returning to top form. He felt Tuesday's performance was one of his best this season.
His teammates agreed.
''He made some huge saves,'' Oshie said. ''This game could have gone the other way, a 5-2 victory (for Phoenix). He came up big and. that's what we expect from him every night.''
''He's a huge reason we won,'' captain David Backes added. ''He got us the two points. We need to play better in front of him. Hopefully, the other 19 of us learned a lesson.''
Oshie recorded his second two-goal game in the last six contests since he was named to the U.S. Olympic team.
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.
The Coyotes fell to 3-8-4 in their last 15 games.
Ekman-Larsson said his team should be able to gain some momentum from a strong third-period effort that simply fell short against a hot goalie.
''I think this is a step in the right direction,'' he said. ''This was our best period in a long time.''
Smith fell to 15-13-8. He has not won since Dec. 21 covering nine appearances.
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.