Cade McNown, off the mark much of the night, still passed for two touchdowns and ran for another as UCLA (4-0 overall, 2-0 Pac-10) won its 14th in a row, the longest winning streak in Division I after Nebraska's 19-game streak was ended by Texas A&M earlier in the day.
Foster, who rushed for 118 yards in 20 carries, had scoring runs of 37 and 1 yards in the first half and Brown, with 91 yards in just nine carries, scored on runs of 54 and 20 in the fourth quarter.
Trailing 28-24 with 6:15 left in the third quarter, the Bruins scored 28 consecutive points in a devastating 6-minute, 10-second span to win in Tucson for the first time in 10 years.
It might not be UCLA's last trip to Arizona this season. The Bruins are poised to move up to No. 2 with Nebraska's loss and could be in Tempe for the national championship game in the Fiesta Bowl on Jan. 4.
UCLA broke the game open with three big scoring plays early in the fourth quarter, McNown's 64-yard pass to Danny Farmer and Brown's scoring runs.
Arizona (5-1, 2-1) had its nine-game winning streak snapped as UCLA shut down the Wildcats' ground game, forcing the Wildcats to pass.
The game-breaking touchdown came early in the fourth quarter when McNown executed a perfect play fake, then hit wide-open Farmer over the middle on a 64-yard scoring play that put UCLA up 38-28 with 11:18 to play. It was McNown's 50th career touchdown pass, tying Tom Ramsey's school record.
After Arizona drove into UCLA territory, the Wildcats decided against a punt and Michael Johnson missed a 49-yard field goal, his first try of the season. UCLA took over on the 32 and, moments later, Brown raced 54 yards for the score that made it 45-28 with 9:33 to play.
On Arizona's next possession, Tony White intercepted Keith Smith's pass at the Wildcats' 20, and Brown scored on the next play to make it 52-28.
UCLA never led until Chris Sailer's first field goal of the season, a 41-yarder, made it 24-21 with 11:27 left in the third quarter. The score was set up by Ryan Roques' interception of Ortege Jenkins' pass and 39-yard return.
Jenkins, who shares quarterback duties with Smith, brought Arizona back, completing a 30-yard pass to Jeremy McDaniel on third-and-20, a play in which the Bruins' coaching staff argued that the receiver's foot was on the out-of-bounds line when he caught the ball.
McDaniel, who also caught a 15-yard touchdown pass in the first half, then made a diving catch as he crossed the goal line on a 28-yard pas from Jenkins and the Wildcats regained the lead at 28-24 with 6:15 left in the third quarter.
Foster's 45-yard kickoff return gave the Bruins the ball at UCLA's 47, and the Bruins chewed up 5:42 in a 13-play scoring drive that ended with McNown's 3-yard run, giving UCLA the lead for good 21-28 with 20 seconds left in the period.
The game, played before a sellout crowd of 58,738 the fourth-largest ever at Arizona Stadium, marked the first time in seven years that two Pac-10 teams ranked in the Top 10 had met.
The Wildcats, playing before their first home sellout crowd in two years, were coming off a thrilling 31-28 victory at Washington, where Jenkins' somersaulted into the end-zone for the game-winning score.
For awhile, this one had almost as many thrills.
In a wild first half, Arizona took the lead three times but UCLA answered on each occasion for a 21-21 tie at the break.
Foster, a 6-foot-1, 205-pound freshman just 18 years old, made the most of the increased playing time he got because Lewis was suspended for the game because of an off-campus fight.
Foster rushed for 94 yards in 10 carries in the first half.
Arizona used a fake punt to set up its first touchdown.
On fourth-and-eight from the UCLA 37, punter Ryan Springston threw a perfect pass to A.J. Brown at the Bruins' 1 to set up the first of Kelvin Eafon's two short touchdown runs and the Wildcats led 7-0 with 4:57 left in the first quarter.
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