Thomas Chabot fed a pass to Cousins at the top of the crease, where he redirected the puck past Karel Vejmelka to give Ottawa a 3-2 lead.
Shane Pinto and Michael Amadio each had a goal and an assist, and Fabian Zetterlund also scored for the Senators (11-6-1), who have won two straight and three of their past four. Samuel Ersson made 30 saves.
Clayton Keller had a goal and an assist, and Barrett Hayton scored for the Mammoth (10-7-1), who have lost two in a row (0-1-1) and are 2-2-1 on a six-game road trip. Vejmelka made 17 saves.
Zetterlund scored with one second remaining on the power play to make it 1-0 for the Senators at 5:27 of the first period. Stephen Halliday fed Zetterlund above the right face-off circle, where he buried a wrist shot past Vejmelka.
Keller tied it 1-1 at 9:57, skating in on the rush and knocking in his own rebound past Ersson.
Keller has recorded at least one point in all five games on Utah’s road trip (one goal, eight assists), and has 13 points (two goals, 11 assists) in eight of his past nine games.
Amadio put the Senators up 2-1 at 6:29 of the third period, finishing a pass from Claude Giroux into an open net off a 3-on-1 rush.
Hayton responded to tie it 2-2 at 9:53 when he set up in the slot and tipped a Keller shot under Ersson's left arm.
After Cousins gave the Senators the late lead, Pinto added an empty-net goal at 19:44 for the 4-2 final.
