Williams set a new NCAA record with his 34th career 100-yard rushing day for the Tigers (7-5), who ended the season on a three-game winning streak and improved to 4-1 all-time in bowl games.
Williams surpassed Pittsburgh's Tony Dorsett and Ohio State's Archie Griffin for the all-time NCAA mark.
Maurice Avery passed for 170 yards on 7-of-13 throwing.
Memphis out-rushed Akron 346-47, but the Zips held the edge in passing yardage, 455-170.
Luke Getsy completed 34-of-59 passes for a Motor City Bowl record 455 yards with four touchdowns for the Zips (7-6), who were making their first ever Division I-A postseason appearance.