The Rams beat Brown 31-28 a month ago for their first win of the season before dropping three straight games.
Rhode Island (2-7, 0-5) will return to Northeast Conference play next Saturday at William & Mary (2-6, 0-4).
Priore was 16-of-25 passing with one interception. Aaron Parker hauled in eight of those passes for 126 yards and a touchdown.
The Rams forced five turnovers with Malik Gavek returning an interception 30 yards for a score to take a 21-7 lead early in the third quarter. Gavek also had a career-high 14 total tackles, well above his previous high of five in one game, and forced a fumble. Momodou Mbye and Rashod Dickerson also each picked off a Christian Carter pass.
Matt Brehon led Merrimack (4-5), rushing for 107 yards and one score.
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