Colorado (23-10) led by as much as 11 before the Bears made a late run to make it close.
The Buffaloes went ahead 58-54 when Booker hit two free throws with 12.1 seconds left, but Eli Stalzer only hit 1 of 2 free throws after Justin Cobbs scored on a layup. Cal raced down the floor to get off a potential tying 3-pointer, but Cobbs' shot came up short.
Josh Scott scored 11 points for the Buffaloes, who will face No. 4 Arizona in the semifinals Friday night.
Cobbs finished with 21 points, five assists and four rebounds. Tyrone Wallace added 13 points for Cal (19-13), which shot 5 of 22 from 3-point range.
After Arizona won the first quarterfinal in a blowout, the Buffaloes and Bears faced off in a matchup of NCAA bubble teams.
Cal lost four of its final six games, but earned the Pac-12's fourth seed and a bye in the tournament by outlasting Colorado in overtime last Saturday in Berkeley.
Colorado has been inconsistent since leading scorer Spencer Dinwiddie went down with a knee injury in January and closed the regular season with three losses in four games, putting its NCAA hopes in a bind.
The Buffaloes got past their first-round Pac-12 game, but it was much harder than anticipated; Colorado never was able to shake last-place Southern California and had to grind out a 59-56 win to earn a shot at Cal.
The Buffaloes were sharp at both ends early against Cal, building an 11-point lead midway through. Colorado dominated the Bears on the glass -- a 21-12 advantage -- did a good job getting out to their shooters, holding Cal to 2 of 12 from 3-point range to lead 31-22 at halftime.
Cal quickly chipped Colorado's lead down to three, but the Buffaloes stretched it back out to 10 by hitting 7 of their first 10 shots.
The shots stopped falling for a while and a scoreless drought of 5 minutes allowed Cal to pull within one after Wallace scored on three straight layups.
Colorado pulled it out, enhancing its NCAA tournament chances while likely sending the Bears to the NIT.