B.J. Crombeen scored a goal and Brad Boyes had three assists for the Blues, who scored three times in the second period to go up 4-2.
Kyle Turris scored on the power play with less than four minutes left in the second to cut the lead to 4-3, but neither team managed to score the rest of the way. Turris also had an assist, while Ed Jovanovski and Shane Doan had a goal each for the Coyotes -- Doan logging his 13th goal of the season.
Manny Legace made 23 saves for St. Louis -- 11 in the third period.
Ilya Bryzgalov allowed four goals on 30 shots for Phoenix.
St. Louis won for just the second time in its last seven home games. Phoenix lost for just the second time in its last six games overall.
Notable deaths of 2014 [PHOTOS]