Smith stopped all 15 shots he faced in the final period, earning his ninth win of the season while keeping the Coyotes in the game in the late going.
Bissonnette's goal midway through the second period came only 66 seconds after the Coyotes' Radim Vrbata had knotted the contest 3-3.
Vrbata added an empty-netter for Phoenix, which improved to 3-1-0 on a five-game road trip.
Luke Adam and Patrick Kaleta scored and Jhonas Enroth stopped 25 shots as Buffalo saw its five-game winning streak snapped.
Celebrity Couples of 2014 [PHOTOS]