Cobbs' shot, which came after the Golden Bears ran nearly all of the final 26 seconds off the clock, hit nothing but net.
Cobbs finished with 14 points and Allen Crabbe had 12 for Cal, which has won four straight.
Arsalan Kazemi had 11 points and a season-high 18 rebounds for the Ducks, who lost their 11th straight game to the Bears. Carlos Emory scored 13 points for Oregon, which hasn't beaten Cal since Feb. 9, 2008.
Oregon, which led 26-21 at halftime, was up 46-43 with 2:06 to play when Robert Thurman recorded a three-point play for Cal on a dunk and free throw to tie it.
The Ducks had a turnover and two missed shots in their final possessions.
Oregon is tied with Arizona for the Pac-12 lead, while third-place Cal continued its climb with its sixth win in seven games.
Cal trailed by 11 points in the first half but came back to tie the score at 29 on a dunk by Thurman 4 minutes into the second half.
Oregon went back up 37-33 on a free throw and 3-pointer by E.J. Singler, but the Bears followed with a 6-0 run and Cobbs hit a jumper to put them up 39-37 with 7:12 to play. It was Cal's first lead since early in the first half.
Trailing 41-39, Oregon followed with five straight points to take a 44-41 advantage with 3:30 to play, setting the stage for Cal's final heroics.
The Ducks led 22-11 late in the first half but scored just one field goal over the final 5:46 and Cal took advantage with a 10-2 run to pull within 24-21.
But Kazemi jammed home a dunk in transition off a steal with 1:18 remaining to give Oregon a five-point lead at halftime.
It could have been worse for the Bears, except Singler's deep 3-pointer at the buzzer was waved off when Emory was called for basket interference.
Kazemi had 14 rebounds and six points in the first half, and Emory sparked Oregon early after Cal scored the first six points of the game.
The senior forward came off the bench to score nine points in a 16-2 run that put the Ducks up 16-8 at the 10:18 mark.
Colorado 60, Utah 50
BOULDER, Colo. -- Spencer Dinwiddie scored 13 points and had a key block in the late going, helping Colorado pull away.
Sabatino Chen added 12 points and Andre Roberson had 10 as Colorado rebounded from its overtime loss to Arizona State last weekend despite missing freshman star Josh Scott, who sat out with a concussion suffered in the game against the Sun Devils.
Stanford 82, Oregon St. 72
CORVALLIS, Ore. -- Josh Huestis had 20 points and 11 rebounds and Stanford pulled away down the stretch.
Dwight Powell had 14 points and 11 rebounds. His driving dunk with 1:09 to go gave the Cardinal a 78-69 lead.
Huestis had just four points and one rebound in the first half, after which Oregon State led 35-34. Chasson Randle scored 12 of his 13 points in the first half to keep Stanford in it. The Cardinal led nearly the entire second half.
Andy Brown also scored 13 for Stanford, and Aaron Bright had 12 points and six assists.
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