Williams ran for 53 yards on 14 carries for the Big Green (2-1, 1-0 Ivy League) and was 13-of-23 for 107 yards passing.
Kyle Bramble's touchdown run late in the first quarter put Dartmouth in a 7-7 tie with the Quakers (0-3, 0-1) with 2:08 left in the period. Two plays into Penn's next drive, Troy Donahue intercepted an Alek Torgersen pass, setting up a 9-yard TD run by Williams five plays later and the Big Green led 14-7.
Williams ran for two more scores in the second quarter - from 24 and 11 yards - to give Dartmouth a 28-10 halftime lead.
Alex Gakenheimer sealed the win for the Big Green with a 35-yard field goal in the fourth quarter.
Torgersen was 40-of-58 for 350 yards and a touchdown for the Quakers.