After New Jersey's Damien Brunner came up empty to start the shootout, Boedker followed with a nifty backhander over Martin Brodeur before Thomas Greiss turned away the final two Devils to send Phoenix to its second straight win.
Kyle Chipchura and Chris Summers supplied a goal and an assist apiece, while Greiss finished with 26 saves for the Coyotes, who remained locked in the second wild-card spot in the Western Conference.
Adam Henrique and Ryane Clowe each lit the lamp for the Devils, who have lost an NHL record 13 consecutive shootouts dating back to last season. Brodeur registered 25 saves in the setback.
Despite the loss, New Jersey moved within four points of an Eastern Conference wild-card spot. Columbus, Detroit, Washington and Toronto all sit tied for the two spots with 80 points.