Taj Benning, who finished with 13 points, scored the final six points for the Stags.
Drew Lowder's layup for Holy Cross with 45 seconds remaining in the second half tied the game at 58 and neither team scored again in regulation.
In overtime, the Crusaders went nearly four minutes without scoring but trailed just 62-60 after Connor Niego scored in the paint. Benning hit a jumper and, later, two free throws, to put the Stags up 66-60, Lowder hit a 3-pointer and Benning wrapped up the victory with two more free throws.
Benning had 13 points and six rebounds for Fairfield (1-2). Wassef Methnani added nine rebounds. Chris Maidoh had three blocks.
Lowder had 16 points and six assists for the Crusaders (0-3). Niego added 14 points and three blocks. Austin Butler had 12 points and six rebounds.
Fairfield faces Loyola (Md.) on the road on Sunday. Holy Cross faces Northeastern at home next Tuesday.
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