But, Buffalo struck back on the power play courtesy of Tage Thompson, who found the back of the net with 1:36 left before the break.
It was 3-3 heading into the third period.
Skinner completed his hat trick with a tally at the 8:16 mark of the stanza, before adding his fourth goal of the afternoon with 1:46 left in regulation.
That's the way this one finished.
Up next for the Canadiens is a matchup against the St. Louis Blues on Thursday night at the Bell Centre.
Puck drop is 7:00 p.m. ET.