The Coyotes, winners of four in a row, can claim the division with a win at Minnesota in their regular season finale on Saturday.
Playoff-bound Phoenix lead the division on 95 points, with Los Angeles and San Jose on 94. The Kings play at the Sharks on Saturday.
"It's an honour and a privilege to be in the playoffs but our goal is to win the division," Coyotes defenseman Keith Yandle said. "It's something that we have to embrace and get those two points.”
Phoenix netminder Mike Smith made 31 saves but saw his shutout streak end at 234 minutes, 25 seconds with Patrik Berglund's equalizing goal in the first period.
"He's been so big for us," Coyotes' Shane Doan said of Smith. "We haven't played so well in the last three games. We wanted to give him a little break. It was nice to give him more than one goal to work with."
Yandle put the Coyotes ahead early in the first, and after the Blues' Berglund made it 1-1, Radim Vrbata and Doan scored 2:10 apart in the second to put Phoenix in command.
Mikkel Boedker wrapped up the scoring midway through the third.
Winning the division title would have other implications for the Coyotes, said coach Dave Tippett.
"It's home ice in the playoffs," Tippett said. "We've been talking about this for a long time, that we want to build to be a playoff team. We put ourselves in a position to do that."
The defeat ended the Blues' hopes of winning the Presidents' Trophy as the National Hockey League's top regular season team.
They now need to win at Dallas on Saturday and hope Vancouver lose to Edmonton to finish top of the Western Conference.
"There's still a chance, there's still something to play for," Blues defenseman Alex Pietrangelo said. "We've got a lot of fighters on this team and we're going to keep doing what we do."
Vancouver lead the West on 109 points and St Louis has 107.