Buffalo won for just the 15th time this season.
Ryan Miller gave up two goals in the span of 18 seconds of the first period that allowed the Coyotes to take a 2-1 lead.
Phoenix could not manage another goal, however, and Buffalo came back to tie it on a power-play score from Steve Ott early in the second period.
It remained a 2-2 game until Girgensons scored for the fifth time this season. Buffalo has just nine victories in regulation or overtime this year, six fewer than any other team in the league. The Sabres' other six wins have come in shootouts.
Miller made 38 saves while Buffalo's three goals came against Thomas Greiss on 25 shots.