Anchorage took the lead for good at 47-44 on Thompson's 3-pointer with 7:51 left. It sparked a 12-2 run and Thompson scored eight points during that stretch.
Max Guercy made four free throws to pull the Owls (1-5) within 59-52 with 1:18 to play, but Rice would not get closer.
Thompson shot 6 of 9 from 3-point range. Brian McGill added nine points, eight rebounds and 10 assists for the Division II Seawolves.
Rice jumped out to a 10-3 lead and led by 12 midway through the first half. The Owls shot 1 of 11 from the field after opening the second half with eight straight points to take a 40-35 lead.