Davidson (3-4) took a 35-19 lead at halftime but saw its advantage cut to 56-54 with 4:30 left. But the Wildcats closed the game with an 11-2 run.
Luka Brajkovic scored 10 of his 13 points during the second half for Davidson, which will play Temple in Sunday's fifth-place game.
Davidson went 9 for 24 from 3-point range after having its 809-game streak of making at least one end after missing all 15 tries in a 73-63 loss to Marquette in the first round on Thursday.
After shooting 27 percent in Thursday's 54-47 loss to Southern California, Fairfield converted 48% (24 of 50) in Friday's game.
Fairfield goes against Texas A&M in Sunday's seventh-place game.
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