Jaroslav Halak made 20 saves to keep the Coyotes at bay and get the Blues back in track after their seven-game winning streak was halted by Vancouver on Friday.
Oshie whistled a slap shot from the right circle past Mike Smith in the first period to open the scoring and then made it 2-0 at 12:54 of the second period on a power-play wrist shot.
Oliver Ekman-Larsson scored the only Phoenix goal on a power-play at 19:12 of the second period. Phoenix threw eight shots at Halak in the third period, but could not score.
Celebrity Families of 2014 [PHOTOS]