Cousins had 24 points and 20 rebounds, and the Kings had their best defensive performance of the season Sunday night in an 88-80 victory.
The Kings, who came in allowing a league-worst 109.6 points per game, easily surpassed their previous best of 88 points allowed, shutting down a Knicks team that played without its leading scorer.
"It was not a stellar basketball game, but for us to get a win on the road is always a happy place," Kings coach George Karl said.
Cousins emerged the winner in a good big-man duel with Lopez, who finished with 23 points and a career-high 20 rebounds.
"That was a fun battle," Cousins said. "You really don't get a chance to see those type of battles with the bigs anymore, it's so much of a guard game. We battled for a full game so it was a lot of fun."
Cousins played through his usual frustrations with the officiating and even a security guard, pushing him after he bumped into Cousins while Rajon Rondo was trying to separate his teammate from the officials at midcourt.
"Actually I think he was trying to remove me from talking to the refs, so he kind of put his hand on my back and tried to move me forward," Cousins said. "So I don't think it was that big of an issue, honestly."
New York fell to 0-8 this season without Anthony, who was still bothered by symptoms of a migraine that he began suffering from Saturday night in a loss at Washington.
Interim coach Kurt Rambis said the Knicks appeared sluggish when they arrived earlier Sunday after the long trip, and that appeared to carry over into the start of the game. The Knicks managed just 5-for-22 shooting and 12 points in the first quarter, falling behind by 16.
"We had three quarters of scoring under 20 points that had a lot to do with, to me, guys looked tired," Rambis said. "There are a lot of shots that our guys normally get, normally make, but when their legs are tired, they're just short."
New York came right back with 35 points in the second, cutting the Kings' lead to 50-47. But it was too much Cousins and the Kings in the fourth quarter.
Rudy Gay scored 17 points for the Kings, who won for just the second time in nine games.
Kings: Rookie Willie Cauley-Stein missed the game with flu-like symptoms. After having no fast-break points in a game for the first time in nearly 10 years Friday at Detroit, the Kings had 12 Sunday.
Knicks: The Knicks fell to 0-17 when scoring under 90 points. ... Forward Kevin Seraphin sat out with a sore left foot. X-rays taken Sunday night were negative.
The Knicks recalled forward Cleanthony Early from Westchester of the NBA Development League, but he didn't play. Early hasn't played for the Knicks since getting shot in the right knee during a robbery on Dec. 30, and said he felt "very fortunate and very blessed" to back on the floor.
"I'm doing pretty good," Early said. "As far as the knee, the injury is pretty much 100 percent. Just got to get my conditioning back up."
Karl coached Anthony in Denver, so he knows how different a team can look without him. He said Anthony's absence made it easier to defend the Knicks' triangle offense.
"We kind of knew where they were going a lot of times and disrupted it somewhat," Karl said.
"You take Melo out of the scenario, you can be a little more chancy and risky because you don't get maybe blown up because of your decisions."
Kings: Visit Chicago on Monday night.
Knicks: Visit Chicago on Wednesday night.
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