Nick Schmaltz, who assisted on the goal, scored seven points (three goals, four assists) in the seven games. The goal came after Blues forward Zach Sanford turned over the puck in the neutral zone.
"I thought we did a good job of pressuring them," Keller said. "Even after we got the lead, we did a good job of staying on them, forechecking, just playing the same way whether we were losing or winning."
Kuemper's shutout was his first of the season and the 19th of his NHL career.
"It was a 1-0 game, it was a mucking-type game and you've got to be able to close them out and we did," Coyotes coach Rick Tocchet said. "Darcy never has a bad effort, he's always there for us and he was again. … He was terrific."
Five of the seven games were decided by one goal.
"Every game was tight," Kuemper said. "We were able to pull it out, grind it out and it was a big win. Obviously it's going to raise our game playing against them. It's going to help us moving forward, and I thought we got better every game."
The Blues had four shots on goal during 3:26 of continuous power-play time in the second period, including a two-man advantage for 34 seconds. They were 0-for-2 on the power play and 2-for-23 during the seven games.
"They're a tough team to forecheck, their goalie played well and made the saves he had to," Blues forward Brayden Schenn said. "We worked hard, we competed, and I thought we deserved at least a goal. We just didn't get the results with the goals."