LOS ANGELES — The nadir for the Warriors’ interior defense came on Christmas, when they surrendered 18 points on just 10 shots — most within a few feet of the rim — to the Lakers’ little-known, 21-year-old center, Ivica Zubac.

As Golden State prepares to face Zubac and Los Angeles on Monday night at Staples Center, it finally has someone capable of matching the 7-foot-1, 240-pounder’s size. Those inside the Warriors’ organization believe that DeMarcus Cousins, who made his Warriors debut in Friday’s win over the Clippers, is a more capable defender than his previous stops in Sacramento and New Orleans suggest.

At 6-foot-11, 270 pounds with elite court vision, Cousins is light on his feet and adept at getting into passing lanes. The problem has long been that, with so much offensive responsibility to worry about, he had a tough time putting full effort into his defense. Now the third or fourth scoring option, at best, for Golden State, Cousins can focus more on the other end of the court.

Cousins showed flashes of his defensive potential Friday. Though he fouled out in just 15 minutes, he swatted a shot, nabbed a steal and corralled five defensive rebounds.

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“I thought he was really solid,” Warriors head coach Steve Kerr said. “I mean, he obviously got into a little bit of foul trouble, but he’s quick. He drops on pick-and-rolls and understands how to take a charge, which he did the other night. He understands how to use his hands for steals.

“He’s got very quick hands. He anticipates really well. He sees the game really well, and he just feels it, so that puts himself in a position to succeed.”

Subpar defensive effort has been one of the biggest criticisms of Cousins. His defensive rating has hovered well above 100.00 his entire career, peaking at 110.7 while with the Kings in the 2016-17 season. After Friday’s game, it was at 40.

When Golden State signed Cousins in July, it saw in him the tools to become a solid defender. Though he won’t lead the league in blocks, he offers the Warriors a big, physical presence on the low block, something they have lacked since Damian Jones sustained a potentially season-ending pectoral injury on Dec. 1 in Detroit.

“He’s got good instincts,” said Warriors assistant coach Ron Adams, who oversees the team’s defense. “The big thing with him that we’ve talked to him about is playing with good fundamentals and staying away from the fouls. I thought he got a couple of cheap fouls the other night that shouldn’t have been called. I liked his decisiveness in so many plays. I think he can really take that part of his game and improve it.”

Cousins won’t ever be a world-class defender in pick-and-rolls, but the Warriors just want to make sure he can’t easily be exploited. As he eases back into the grind of NBA games, Golden State is intent to not overload him, asking him to hang back instead of switching on screens. On the couple of occasions he did switch Friday, Kerr was pleased with the results.

“Tonight, he’ll help us,” Kerr said. “Zubac killed us last game, a really skilled big guy in the paint.

“We’ll need (Cousins) against a lot of different matchups. Like all players, he’s got strengths and he’s got weaknesses. It’s our job to accentuate the positive and try to mitigate the weaknesses.”

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com. Twitter: @Con_Chron