The Canadiens were still down by two goals after 40 minutes.
Henri Jokiharju upped Buffalo's lead to 5-2 at the 3:48 mark of the third period.
Tage Thompson put head coach Don Granato's contingent up 6-2 at 6:39.
Skinner added his second tally of the contest at 14:26 on the power play.
That's the way this one finished.
The Canadiens are back in action Wednesday night when they battle the Blue Jackets at Nationwide Arena in Columbus to begin a two-game road trip.