A win by Detroit earlier in the evening officially ended the Coyotes' playoff hopes, but they still managed a triumph over a team that had a lot at stake.
San Jose missed a chance to move past Los Angeles into fourth place in the Western Conference standings, a position that carries with it home-ice advantage in the opening round of the playoffs.
The Sharks are tied with Los Angeles for the fourth spot, the Kings having also lost Wednesday to Detroit.
Los Angeles holds the tiebreak advantage against San Jose, but St. Louis is only a point behind both teams with two games to play.
Thomas Greiss stopped 30-of-32 shots for the Sharks.