Brown, the nation's leading rusher, boosted his per-game average slightly to 164.9 yards as Colorado (5-2, 3-0 Big 12) won for the fourth straight time.
It was Brown's fourth consecutive 100-yard game and fifth of the season, coming one week after he gained 309 yards against Kansas.
In the final two games of the 2001 season, Brown ran for 380 yards and nine touchdowns, including six TDs against Nebraska. Coach Gary Barnett thinks he's even better now.
"He's got that burst that he didn't have a year ago," Barnett said. "When he gets to the hole, he just sort of explodes. It's made him into a really good back right now. There probably aren't many who are much better."
Baylor coach Kevin Steele said the 6-foot-3, 220-pound Brown "is like an offensive lineman in the backfield."
Brown, who's listed as probable for next week's game against Texas Tech, said, "It's mostly a credit to our offensive line and our fullback. They've been playing great the last few games. Anything I do is really a group achievement. They just attach the numbers to my name.
"We won, and that's the only thing that matters to me."
Brown had touchdown runs of 55, 4 and 1 yard. He became the fastest player in Colorado history to reach 1,000 yards in a season, doing it in 143 carries. Rashaan Salaam needed 149 carries to hit 1,000 on his way to 2,055 yards and the Heisman Trophy in 1994.
Baylor (3-4, 1-2) had 251 total yards - compared with 395 for the Buffaloes - and crossed midfield only three times.
The Bears had two scoring threats in the final five minutes, but third-string quarterback Josh Zachry fumbled at the Colorado 20-yard line with 4:55 remaining and threw incomplete in the end zone on the final play of the game.
Baylor was shut out for the second straight game and third time this season.
"That's two weeks in a row of nothing," Steele said. "You don't ever want to be shut out. That's unacceptable. We were just totally inept on offense.
"We missed some tackles early and they got it steamrolling. The defense made some adjustments in the second half and tried to make amends, but it was too much."
Baylor, 0-15 against ranked teams since 1998, entered the game 116th among Division I-A teams - next to last - in turnover margin at minus-14. The Bears were minus-2 Saturday.
Robert Hodge completed 13 of 16 passes for 125 yards and scrambled 34 yards for a touchdown.
Brown ran for 115 yards in the first half, and his three scores helped the Buffs take a 34-0 lead. Colorado outgained Baylor 283-69 in the half, and the quick-striking Buffaloes had four scoring drives of less than two minutes, including 47 seconds and 49 seconds.
On the third play from scrimmage, Brown went off right tackle, got free along the sideline and went 55 yards for a touchdown.
Hodge hit Derek McCoy on consecutive 14-yard completions to set up fullback Brandon Drumm's 1-yard run.
The Bears resorted to some trickery that backfired late in the first period. Aaron Karas lateraled to reserve quarterback Guy Tomcheck, whose underthrown pass was intercepted by safety Rod Sneed and returned 21 yards, setting up Colorado's third touchdown.
Hodge passed 28 yards to Jesse Wallace, and Brown went the final 4 yards on the opening play of the second quarter.
Colorado needed to go only 38 yards on its next series after a shanked 16-yard punt by Baylor's Jeremy Parker. Hodge avoided a sack and scrambled 34 yards for a TD and a 27-0 lead.
After an exchange of turnovers, the Buffs went 52 yards on eight plays for another score late in the half. McCoy ran 20 yards on a reverse, and Brown plunged for the final yard.
The Buffs squandered another scoring opportunity early in the third quarter on a fumble at the Baylor 10, when Hodge botched a handoff to Brian Calhoun.
Colorado drove to the Baylor 18 on its next possession, but Hodge was sacked for a 14-yard loss by Justin Crooks, and a personal-foul penalty after the play forced a punt.
It was Colorado's first shutout since Nov. 13, 1999, when the Buffs defeated Baylor 37-0 in Waco.