Schmaltz made it 4-1 at 13:58 with a backhand from the slot off a pass by Keller.
"I think they work extremely hard," Coyotes coach Andre Tourigny said of the top line. "Today, they had their execution. I don't think they had that since the beginning. They weren't connecting like they did tonight. They connected and they made plays. They were good."
Jason Zucker's power-play goal extended it to 5-1 at 2:09 of the third period. He scored on a one-timer from the right circle.
"We gave up three power-play goals," St. Louis coach Craig Berube said. "Penalty kill wasn't good. Just not clearing pucks, switches that are unnecessary in [the] zone, just giving up easy plays. Execution on the PK.
"... We were flat, all around. Didn't skate, didn't execute anything tonight. We didn't move at all."
Sammy Blais cut the Blues deficit to 5-2 at 3:16, but Durzi scored the Coyotes' third power-play goal at 16:59 with a shot from the point for the 6-2 final.
"I think our goalie was good," Tourigny said. "We had a good performance from all of our D-corps. We put a lot of pucks on net. That was good. I think in general, there was better execution from us."
NOTES: Schmaltz has 31 points (11 goals, 20 assists) in 30 games against St. Louis; Keller, who grew up in nearby Swansea, Illinois, has 26 points (11 goals, 15 assists) in 25 games against the Blues. ... Keller (347) surpassed Morris Lukowich (345) for sole possession of 11th on the franchise’s points list. … Forward Logan Cooley, the No. 3 pick in the 2022 NHL Draft, had an assist for Arizona and has four in four games to start his NHL career. ... The Coyotes will play their home opener against the Anaheim Ducks on Saturday. ... St. Louis has not had the lead at any point this season, a span of 190 minutes. ... Blues forward Pavel Buchnevich missed the game with an upper-body injury.