The kick capped an 11-play, 65-yard drive that was kept alive by a 25-yard pass from Bradlee Van Pelt to Matt Bartz on fourth-and-3 from the Cal 45.
Van Pelt finished with 317 yards passing and 60 yards rushing for the Rams (1-1) while David Alexander had seven receptions for 141 yards.
California (1-2) erased a 20-7 Colorado State lead with two fourth-quarter touchdowns, but couldn't come back again following Babcock's late field goal.
With 1:50 left to play, Colorado State's Ben Stratton intercepted a pass from Reggie Robertson to end the Golden Bears' hopes.
Robertson had three touchdown passes, two to Geoff McArthur in the fourth quarter, and threw for 248 yards.
Colorado State opened the scoring when Babcock hit a career-best 48-yard field goal with 7:48 left in the first quarter.
Cal immediately countered with a six-play 80-yard drive that culminated in a 30-yard touchdown pass from Robertson to Vincent Strang with 4:42 remaining.
The Rams took the lead back on the first play from scrimmage after the kickoff, as Van Pelt connected with tight end Joel Dreesen on an 85-yard pass that put the Colorado State up 10-7. The 85-yard strike was the second-longest pass play in Colorado State's 110-year football history.
The Rams extended their lead to 17-7 on a 25-yard pass from Van Pelt to Alexander, who is averaging 25.8 yards per catch this season, with 12:46 to go in the second period.
Van Pelt finished the first half with six completions in seven attempts for 177 yards and two touchdowns.
The win was just the seventh for Colorado State in 43 games against Pac-10 schools, and the first since Oct. 8, 1994, when the Rams beat Arizona, 21-16.