Cole scores 3 goals in first 5:41 for Canadiens
Cole has 30 goals this season. Patteri Nokelainen also scored in the first period, and Lars Eller added one in the third for Montreal, 4-0-2 against Ottawa.
Jason Spezza, playing his 600th NHL game, scored for Ottawa to reach 30 goals for the fourth time in his career and the first time since 2008-09.
Ottawa goalie Craig Anderson, returning after missing 12 games because of a finger cut, was pulled at the 4:56 mark of the first in favor of Ben Bishop, but was back in to start the second period.
The Senators, 1-3-2 in their last six games, are seventh in the Eastern Conference, two points ahead of Washington and Buffalo
Cole scored on the first shot on Anderson, who had a routine shot go off his glove and into the net only 29 seconds in. Cole then scored off P.K. Subban's rebound to chase Anderson.
Cole completed the hat track at 5:41 against Bishop.
Notes: Montreal defenseman Yannick Weber left after the first period because of a lower-body injury. ... Bishop had made the last seven straight starts for Ottawa. ... Spezza has 608 career points.