Rice got 3-pointers by Bishop Mency and Marcus Jackson near the end of the first half and led 45-37 at the break.
North Texas (9-11, 3-5 Conference USA) chipped away at the deficit and finally pulled even at 58 with eight minutes left.
Rice went almost six minutes with just one free throw and the Mean Green reeled off eight straight points - including Armani Flannigan's tip-in - and held on down the stretch.
Williams was 7 of 12 from the floor with three 3-pointers as North Texas shot 57 percent. Maurice Aniefolk added 15 points, Jeremy Combs had 13 and T.J. Taylor chipped in with 11 points.
Rice (6-14, 3-5 Conference USA) was led by Seth Gearhart's 20 points and Jackson finished with 18 points, including five 3-pointers.