The Blues have won 11 of 13 games and have points in 12 of those.
St. Louis' Carter Hutton stopped 22 shots. He faced only 13 in the first two periods combined, then saved a breakaway attempt by Tobias Rieder early in the third period before Alex Goligoski scored a power-play goal at 14:37.
David Perron added an empty-net goal with 19 seconds left.
The Blues moved closer to locking up a postseason berth, falling short of clinching because the Los Angeles Kings beat the Calgary Flames. St. Louis beat Arizona for the 11th straight time and the third time in 11 days.