St. Louis won its fifth straight, but had to sweat out a comeback featuring two goals from Shane Doan, who brought the Coyotes within one with 21 seconds left.
All four wins in the current St. Louis streak have come at home and the Blues will close out a five-game homestand Sunday against Dallas.
Brad Boyes opened the scoring with 5:52 left in the first period. Erik Johnson scored shorthanded and Alex Pietrangelo added a power-play goal in the second.
Jaroslav Halak survived the third-period assault to make 30 saves and get the win. Ilya Bryzgalov allowed four goals for Phoenix on only 22 shots.