The last time Illinois head coach Lovie Smith participated in a bowl game, he was the secondary coach at Ohio State and calling coverages against Peyton Manning’s Tennessee squad in the 1996 Citrus Bowl.

Twenty-three years later, Chase Garbers put up a Manning-like performance against Smith’s defense, leading Cal to a 35-20 victory in the Redbox Bowl on Monday afternoon in front of a crowd of 34,177 at Levi’s Stadium.

Garbers was 22-for-31 for 272 yards and a career best-tying four touchdown passes. The sophomore added a rushing score in a victory that bookended a season of significant strides for the Bears (8-5).

“I thought he did a great job, an awesome job,” Cal head coach Justin Wilcox said of Garbers. “I think he’s taken that next step. ... He has just continued to work at it, and guys respect him because of how hard he works and his preparation. I thought it really showed today, and I think he’s got a really bright future.”

Cal won a bowl game for the first time since beating Air Force in the 2015 Armed Forces Bowl and for just the second time since the 2008 Emerald Bowl. The Bears were making consecutive postseason appearances for the first time since they played in seven straight bowl games from 2003 through ’09 as Wilcox nudges the program back toward relevancy.

Cal tied for second place in the Pac-12 North this season, its highest finish since the conference was split into divisions in 2011. The Bears also beat Stanford for the first time since 2009 and won games in Los Angeles in consecutive seasons for the first time since 1970-71.

The Bears hadn’t beaten Stanford, USC and UCLA in a two-year span since 1949-50, and it’s likely that similar skids will be snapped if Garbers continues to play like he did against the Fighting Illini (6-7).

Just a year after being yanked at halftime of the Cheez-It Bowl loss, Garbers gave Cal 7-3 and a 14-10 leads with a 4-yard touchdown pass to Collin Moore in the first quarter and a 1-yard quarterback sneak in the second quarter.

In the final seconds of the first half, Garbers made Wilcox’s gamble on a 4th-and-goal from the 3-yard line pay off when he hit Christopher Brown Jr. with a screen pass that led the running back past Illinois linebacker Khalan Tolson and into the corner of the end zone to make it 21-10.

“Honestly, I don’t even remember the play call. Oh right, we scored,” Garbers said. “Chris got open and caught the ball. All I had to do is throw it to him. It’s a pretty easy job, and he did the rest.”

Garbers made it look especially easy in the second half, when Cal pulled away with a 2-yard touchdown pass to Gavin Reinwald and a 6-yard scoring strike to Nikko Remigio.

Chase Garbers’ stats 22-of-31 passing attempts 272 passing yards 5 TDs (one rushing)

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In between all of the short red-zone darts, Garbers mixed in a series of deep passes to Makai Polk (five catches for 105 yards).

The offensive outburst was surprising in a game that was expected to be a defensive struggle and featured two of the nation’s most productive linebackers. The teams had already passed the Las Vegas over-under line of 45 points with 11 minutes to play, and Cal’s Evan Weaver and Illinois’ Dele Harding were quiet by their standards.

Weaver, who entered the game with a NCAA-leading 173 tackles, had nine against Illinois to finish 11 shy of the all-time single-season mark set by Texas Tech’s Lawrence Flugence in 2002. Harding had six to bump his season total to 153.

“The stats come with it, but all I ever cared about this season was getting as many wins as we could,” Weaver said. “I’m happy with eight wins, the most I’ve ever had in college. ... I want to be remembered as one of the building blocks for the future success that this program is going to have.”

Rusty Simmons is a San Francisco Chronicle staff writer. Email: rsimmons@sfchronicle.com Twitter: @Rusty_SFChron