Allen Crabbe had 14 points. Cobbs finished with 10 points, five assists and five rebounds for the Golden Bears (10-6, 2-2 Pac-12), who won for just the fourth time in 10 games after opening the season 6-0.
It definitely wasn't pretty.
California was held without a basket over the final 4:59 but went 11 of 12 at the free-throw line down the stretch to hold off Washington State (9-7, 0-3).
Brock Motum scored 16 points for the Cougars, and Mike Ladd had 12 points and 12 rebounds.
Wallace, a freshman who had been shut out in his previous two games at Haas Pavilion, had seven points in the first half for Cal but did his most effective work down the stretch.
After Royce Woolridge's 3-pointer pulled the Cougars within 52-49 with 5:50 remaining, Wallace grabbed a long offensive rebound and scored on a driving layup. He followed with a short jumper then blocked a Motum layup attempt from behind before adding three free throws as part of a 9-1 run in the final minutes.
California tied a team record with 11 blocked shots, a career-high six from Richard Solomon.
The Bears needed every one to hold off a pesky Washington State team that shot just 33.3 percent for the game but was within 58-51 with 3 1 /2 minutes to play.
But the Cougars went cold following a putback by Ladd and managed only four baskets over the final 12 minutes while losing its third straight following a five-game winning streak.
Neither team played well during a sloppy, mistake-filled first half.
Cal went 9 of 12 from the floor but committed 10 turnovers and was consistently outworked in the paint and outhustled for loose balls. Crabbe, coming off a season-low nine points in the Bears 62-47 loss to Washington on Wednesday, got off to another slow start and had just four points before the break.
Washington State wasn't much better, shooting only 35.7 percent and going 1 of 8 on 3s. Motum had 10 points in the first half, but he also had two turnovers.
Jeff Powers, making his first start of the season, had five for Cal, including a late 3-pointer, while Robert Thurman picked up a loose ball and scored with six seconds remaining to put the Bears up 29-27 at halftime.
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