Luca Del Bel Belluz scored 2 minutes, 28 seconds into overtime to lift the Monsters over host Hartford, 4-3.
The first-place Monsters improved to 14-5-1-0.
Carson Meyer scored two goals, both in the second period, to give him 11 for the season. Cameron Butler also had a goal.
Daniil Tarasov saved 36 of the 39 shots he faced.
Cleveland’s three-game trip continues Dec. 8 at Wilkes-Barre/Scranton.
