Kesler, who had been out nearly two months with a broken right foot, put the Canucks ahead 7 1/2 minutes into the game when he poked in a loose puck after a shot by Mason Raymond.
The contest remained 1-0 until 1 minute was left in the third period. Phoenix had pulled goalie Mike Smith for an extra attacker when the Coyotes' Antoine Vermette scored an own-goal as his errant pass found its way into the empty net.
The tally was credited to Vancouver's Dan Hamhuis.
Schneider made 19 stops in racking up his fifth shutout of the season as the Canucks forged a four-point lead over Minnesota atop the Northwest Division.
Smith turned aside 40-of-41 shots for Phoenix, which remained three points out of a Western Conference playoff spot.