The three goals marked the fifth career hat trick for Tavares, who also tied a career-high with five total points.
Brock Nelson, Peter Regin, Ryan Strome and Brian Strait also scored for New York, which erased a 2-0 deficit and cruised to a fourth win in five games.
Kevin Poulin took over from an injured Evgeni Nabokov in the first period and stopped 13-of-15 shots for the win. Nabokov left with what appeared to a groin strain after yielding a goal on eight shots.
Kari Lehtonen was lit up for seven goals on 43 shots.