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.
UCLA 82, Oregon 63 • In Las Vegas, Jordan Adams scored 15 points and UCLA ran away from Oregon with a big second-half run in the quarterfinals of the Pac-12 tournament on Thursday night.
UCLA (24-8) had a superb night shooting and clamped down on Oregon in the second half to turn what had been a close game into a runaway after halftime.
The Bruins opened the second half with a huge run and kept dropping shots, hitting 57 percent from the floor to advance to Friday's semifinals against the winner of Stanford and Arizona State, who played late Thursday night.
Joseph Young scored 29 points for the Ducks (23-9), who should still be a lock for the NCAA tournament when Selection Sunday rolls around.
• No. 1 Arizona 71, No. 8 Utah 39
• No. 5 Colorado 59, No. 4 Cal 56
• No. 2 UCLA 82, No. 7 Oregon 63
• No. 3 Arizona State vs. No. 6 Stanford, late
• Arizona vs. Colorado, 7 p.m., Pac-12 Network
• Oregon vs. Arizona St.-Stanford winner, 9:30 p.m., Fox Sports 1
• Semifinal winners, 4 p.m., Fox Sports 1