Evans drove in from the right and tucked a backhand around Akira Schmid for the winner after Montreal allowed the tying goal with 3:08 remaining in the third period.
Caufield, who scored his second career hat trick in a 4-3 loss at the Boston Bruins on Saturday, has 11 points (nine goals, two assists) during his longest NHL goal streak.
Phillip Danault scored, and Jakub Dobes made 32 saves for Montreal (29-17-7), which had lost consecutive games for the first time since Dec. 7-9.
Pavel Dorofeyev scored twice, and Schmid made 23 saves for Vegas (25-14-13), which lost 7-1 at the Ottawa Senators on Sunday and is 1-3-1 in its past five games.
Dorofeyev scored his second of the game at 3:08 of the third to tie it 2-2 with a deflection past Dobes’ glove on Ben Hutton’s shot from the left point.
Schmid dove to his left to glove Juraj Slafkovsky’s backhand from the goalmouth during a Canadiens power play early in overtime after Rasmus Andersson was called for tripping with 33 seconds left in the third period.
Dorofeyev gave Vegas a 1-0 lead with an unassisted goal at 8:38 of the first period. He carried the puck along the left side on a 2-on-1 with Braeden Bowman and scored glove side on Dobes with a wrist shot from the left face-off dot.
Danault tied it 1-1 at 4:24 of the second period when he got in the lane of Zachary Bolduc’s turnaround wrist shot from the left point and tipped the puck down and past Schmid glove side.
Caufield reached 30 goals for a second straight season to put Montreal ahead 2-1 at 8:55. He was positioned to the right of the net to get to a loose puck and tuck a backhand inside the post.
He scored a career-high 37 goals last season.
Dobes stuck out his left pad to stop Stone’s shot from the right edge of the crease on a backdoor pass from Jack Eichel on a power play 31 seconds into the third.
The Canadiens are 17-6-0 against Western Conference opponents, including a 4-1 road win against the Golden Knights on Nov. 28.
