The Trojans (1-4, 0-3 Pac-10), who have struggled recently against Washington, forced a 24-24 tie with just under four minutes to play when Carson Palmer hit a streaking Kareem Kelly up the middle for a 58-yard touchdown.
However, the unbeaten Huskies (4-0, 2-0) moved down the field and positioned the ball perfectly for Anderson, a junior who split the uprights to set off a wild celebration.
Anderson improved to 12 of 15 from beyond 30 yards and it was his second field goal of the final quarter. He connected from 25 yards out with 11:13 to play to force a 17-17 tie, the third of four deadlocks in the tightly-contested battle.
It was a dramatic renewel of a rivalry between the two all-time winningest schools in Pac-10 history. USC leads the all-time series, 42-26-4, but Washington has now won seven of the last 10 matchups. Saturday was the first meeting between the schools since 1998.
The victory might also be a sign of good things to come for the Huskies. In the 38 previous meetings since 1960, the winner of this contest has advanced to the Rose Bowl 23 times, although on 15 occasions it was the Trojans heading to Pasadena after the new year.