Franklin, a senior, was 2 yards shy of his career high in rushing yards and tied his career high in touchdowns. Those scores came on runs of 74, 78 and 22 yards.
It was the second 200-yard rushing performance of his career, and he became only the fourth UCLA player to rush for 200 yards in multiple games.
He moved into seventh place on the school's career rushing leaders list with 2,883 yards.
Franklin needs another 849 yards this season to pass Gaston Green for the top spot on that list.