Marcus Thornton finished with 16 points and six assists and Sean Sheldon contributed 11 points and six rebounds for William & Mary (3-1).
Seth Gearhart tallied 14 points and five rebounds and Bishop Mency added 13 points for Rice (1-2).
William & Mary took a 38-30 lead into the intermission and built on it in the second half with a 12-4 run capped by a Terry Tarpey layup to go up 14 with 11:16 remaining. But the Owls scored 12 straight ending with a 3-pointer from Dan Peera, his second in a row, to bring them within three points. A pair of free throws from both Tarpey and Marcus Thornton in the final 10 seconds sealed the win for the Tribe.