Tate scored on runs of 75, 58, 47 and 28 yards as the Wildcats (3-2, 1-1 Pac-12) won their third straight game in Boulder. He eclipsed the old mark of 322 yards set by Northern Illinois' Jordan Lynch in 2013.
The Wildcats rung up 425 of their 567 total yards on the ground. Tate was 11-of-12 passing for 142 yards and a touchdown.
Tate, who entered in the first quarter after starter Brandon Dawkins was banged up, did his rushing damage on just 14 carries.
Senior running back Phillip Lindsay rushed for a career-high 281 yards and three touchdowns for Colorado (3-3, 0-3). It marked the ninth 100-plus yard game of his career and second 200-yard effort.
It was the first time a Pac-12 game featured two players with at least 280 rushing yards.
Tight end Chris Bounds, who entered the game with two career catches, hauled in a pair of touchdowns for Colorado. Wide receiver Bryce Bobo added another receiving score from Steven Montez, who was 19 of 31 for 252 yards.
Colorado tied the game at 14, courtesy of a 19-play, 85-yard drive that took 9:34 of the second quarter and culminated with a 1-yard Lindsay rushing touchdown. Arizona countered by using three plays to go 68 yards in less than a minute to regain the lead at 21-14 heading into halftime with a 13-yard Shun Brown touchdown catch.
Tate's 75-yard run with 13:06 remaining gave the Wildcats a 42-28 lead with 13:06 left. Colorado rebounded when Montez connected with Bounds for a 39-yard score.
The Buffaloes trimmed the deficit to 45-42 on Lindsay's 11-yard touchdown run with 5:04 but never got the ball back as Arizona covered 55 yards on eight plays to run out the clock.
Colorado committed 12 penalties for 110 yards while the Wildcats were flagged twice for 10 yards.