Toledo (12-8, 4-3 Mid-American) used a 9-4 run midway through the first half - sparked by Stuckey Mosley's 3-pointer - to lead 34-27 at the break.
The lead reached 10 on Williams' 3-pointer two minutes after intermission. Willie Moore's layup capped an 8-0 run for Miami which tied it at 65 with 1:11 left, but Williams made 3 of 4 from the line and Miami missed its last two shots. Williams' dunk as time ran out was the exclamation point on the win.
Julius Brown and J.D. Weatherspoon scored 13 points apiece for Toledo, which shot 49 percent as a team. Nathan Boothe added 10 points, five boards and five assists.
Miami (7-13, 2-5) was led by Eric Washington's 16 points. Logan McLane added 14 points and seven boards.