Rice (10-16, 7-7) is battling for one of four remaining spots in the Conference USA tournament. Eight teams have clinched berths, including North Texas, which clinched by beating Florida International on Saturday.
Guercy finished with a career-high 25 points on 9-of-13 shooting from the field and 7 of 7 from the free-throw line. Gearhart, the co-Conference USA Player of the Week, had 24 points and Marcus Jackson contributed 10.
The Owls shot 49 percent from the field, knocking down 25 of 51 field goals, including 8 of 19 from beyond the arc.
Solomon Poole scored 22 points to lead Florida Atlantic (8-17, 1-13), which shot 50 percent from the field, 24 for 48, including 7 of 16 from distance.