Schmaltz added a backhand goal from the slot off a pass by Keller at 13:58 to make it 4-1.
"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, a one-timer from the right circle at 2:09 of the third period, made it 5-1.
"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 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 St. Louis deficit to 5-2 at 3:16.
Durzi added Arizona's third power-play goal with a shot from the point at 16:59 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, Ill., 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 all-time points list. … Forward Logan Cooley, the third pick in the 2022 NHL Draft, had an assist for Arizona and has four in four games to start his NHL career. ... St. Louis has not had the lead at any point this season spanning 190 minutes. ... Blues forward Pavel Buchnevich missed the game with an upper-body injury. ... Toropchenko played in his 100th NHL game.