Crabbe couldn't find his shot, as the Golden Bears' porous defense surrendered three double-digit first-half leads.
Yet, just when they looked down for the count, Crabbe and Cobbs took over and dragged Cal (4-0) to a 73-70 win over Drake in the quarterfinals of the DirecTV Classic at the Anaheim Convention Center.
Cobbs scored a game-high 21 points, including the go-ahead jumper from the left of the free throw line with 1:09 left to play, then added two free throws with 17.2 remaining after Bulldogs forward Ben Simons threw up an off-balance three-pointer.
Simons had another chance to tie the game in the closing seconds, but his corner three rimmed out. Jordan Clarke collected the offensive rebound and was fouled by Richard Solomon, but missed the first and Robert Thurman rebounded the second.
"We had our hands full," Cal head coach Mike Montgomery said. "We were in trouble. They gave us all we wanted."
Drake (1-2) led by nine points with 6:59 to go, but Cal was able to get out in transition for a Crabbe three from the corner and guard Brandon Smith's layup and foul shot for a three-point play.
Cobbs also knocked down four free throws during the 12-2 run. Cal finished the night 20-26 from the stripe, Cobbs making 11 of his 13 tries, while Drake was 15-26.
"At the end of the game, when it counted the most, they made shots," Drake head coach Mark Phelps said.
That was especially true of Crabbe, who entered the game as the nation's fourth-leading scorer at 26.7 points per game, but had 2 points at halftime. The junior turned it on after the break, adding 13 as he made 4-6 shots from the field.
Cal needed that kind of production from its stars to compensate for another poor offensive showing from the front line.
Richard Solomon was solid, scoring 10 points in just 12 minutes because of foul trouble, but he, Thurman, and David Kravish were 9-23 from the floor combined. They also struggled on the defensive end, leading Montgomery to say, "I didn't think they were very good."
Still, Cal overcame plenty of obstacles to advance and face Georgia Tech on Friday night (9 p.m., ESPN2), including the loss of redshirt sophomore guard Ricky Kreklow in warm-ups.
Kreklow injured his surgically repaired right foot and spent most of the first half icing it. Montgomery said he did not expect to have the transfer from Missouri available the rest of the weekend.
Dan Greenspan is the publisher of Cal Sports Digest and writes about the Pac-12 for Fox Sports Next. Follow him on Twitter @DanGreenspan.