Colorado (23-13) set a school record for wins and advanced past the second round of the NIT for the first time since reaching the semifinals in 1991. The Buffaloes will play the winner of Sunday's game between Fairfield and Kent State on Tuesday in Boulder.
Jorge Gutierrez had 16 points and Harper Kamp 14 for the Bears (18-15), who played without starting center Markhuri Sanders-Frison. Cal's leading rebounder, Sanders-Frison dislocated his right shoulder in practice on Tuesday. He was on the bench with his arm in a sling.
With 13 points from Burks, the Buffaloes led by nine midway through the first half, but the Bears' accurate long-range shooting got them back in the game. Cal hit six 3-pointers in the final 7:55 to cut the lead to 37-34 at the break.
"They got a lot of 3s in transition," Colorado junior Austin Dufault said. "They shot 6 for 10, so they were hot."
Gutierrez, who averages 14.6 points a game, scored all of his points in the first half. He went down hard with 14:24 left in the game and lay on the floor for several minutes before walking to the bench. He didn't return.
"He fell and sprained his ankle and hit somebody's knee with his head," Cal coach Mike Montgomery said. "So he got a double whammy."
Colorado's lead grew from 12 to 17 when Gutierrez left.
"It was a big blow," Colorado coach Tad Boyle said. "He's the heart and soul of that team. When he went down they were in trouble."
Colorado led 54-46 early in the second half when the game opened up for the Buffaloes. Higgins was intentionally fouled on a layup and hit the free throw. Burks hit two more free throws, and after a free throw by Cal, Higgins hit a jumper and Marcus Relphorde nailed a 3 to make it 64-47 with 13:35 left.
"That was a huge turnaround," Montgomery said of the intentional foul call on Emerson Murray. "It turned out to be a six-point play, which is huge given the circumstances."
Cal went on a 9-0 run to get within eight, and the lead hovered there until Colorado pulled away in the last 5 minutes. Burks' three-point play with 3:24 left made it 85-69 and the Buffaloes cleared the bench.
Higgins scored 19 points in the second half.
"He's been playing at a really high level," Boyle said. "He and Alec have really put this team on their shoulders."
The Bears had no answer for Colorado's 1-2 punch.
"We just didn't make plays," Cal freshman Allen Crabbe said. "We had a couple of runs and they just came back and made their run."
The Buffaloes lost starting point guard Nate Tomlinson to a sprained left shoulder early in the second half and his status for Tuesday is unknown. Redshirt freshman Shannon Sharpe had six points in relief of Tomlinson.
"He had good minutes tonight, so if Nate can't go we're going to need some minutes out of Shannon," Boyle said.