Blues defenseman Justin Faulk's apparent goal 5:05 into the game was quickly overturned because forward Robert Thomas brushed Vejmelka's glove just before the puck went in.
Thomas later took a stick to the midsection at 4:38 of the second and missed the rest of the game with a lower-body injury. Berube had no update afterward.
St. Louis' three consecutive losses have come against the below-.500 Chicago Blackhawks, Buffalo Sabres and Coyotes.
"Those are three teams where, if you look at the schedule, and with all due respect to every team -- anybody can beat anyone -- those are the games that you have to play better in and get points," Schenn said. "To come away with zero points it's obviously tough, and now you find yourself digging a hole again."
The Coyotes were without defenseman Shayne Gostisbehere (upper-body injury), but Crouse (four games) and forward Matias Maccelli (16 games) each returned from injury.
"Honestly, it was good to have some guys back in the lineup, two really good players who give us balance and more pace in our game, and shorter shifts for everybody," Tourigny said. "It changes a lot of things, but the most important thing was our mindset right from the beginning."
NOTES: St. Louis was 0-for-3 on the power play and is 2-for-22 in its past seven games. Arizona had allowed a power-play goal in eight consecutive games. … Schmaltz has four goals and three assists in his past three games. He has 23 points (eight goals, 15 assists) in 27 games against St. Louis; the multigoal game was his first of the season and 10th of his career. ... Crouse had an assist in 13:50 of ice time; Maccelli had one shot in 13:37.