The Coyotes, winners of four in a row, can claim the division with a win at Minnesota in their regular season finale on Saturday.
Phoenix lead the division on 95 points, with Los Angeles and San Jose on 94. The Kings play at the Sharks on Saturday.
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.
Mikkel Boedker wrapped up the scoring midway through the third.
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.
Vancouver lead the West on 109 points and St. Louis has 107.
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Peter Rutherford)