Bryzgalov gave up four goals on 11 shots Monday against the New York Rangers but turned aside all 32 attempts he saw against the Blues. It was his third shutout of the season and 11th of his career.
Phoenix won its second straight and has captured five of its seven road games.
Daniel Winnik opened the scoring 2:48 into the second period with a slapshot and Taylor Pyatt put a backhander past Ty Conklin for his first goal of the season 2:54 into the third.
Conklin stopped 27-of-29 shots. St. Louis won its opening two games of the year against Detroit in Sweden and has not won back-to-back contests since.
Copyright 2009 by United Press International.