LOS ANGELES — The Lakers and Knicks both got damaged Tuesday at Staples Center.

The Lakers won in a 117-87 rout, but the Knicks delivered the purple and gold a physical pounding on Anthony Davis and Kentavious Caldwell-Pope.

The Lakers superstar contested a Julius Randle layup with 2:45 left in the third quarter and fell violently on his back. Davis stayed down for several minutes while teammates huddled around the fallen big man.

X-Rays were negative and the Lakers termed the injury “a sacral contusion.” He is expected to have an MRI exam and will not make the Lakers’ upcoming two-game road trip.

“Health is first,” LeBron James said. “If he has to miss some time, it’s next man up.

When he got to his feet, Davis gingerly hobbled off the court on his own power to the locker room area, where a gurney was waiting.

The violence was witnessed by longtime Lakers’ superfan Jack Nicholson, who rarely shows up anymore and whose presence shows the franchise is back.

Randle is a former lottery pick by the Lakers and the franchise decided not to re-sign him in 2018 to keep cap flexibility for 2019 that helped net Davis.

Randle was not made available for comment after the game because of what team officials called “personal reasons.” He was hurried into a private room and when he emerged he looked upset. It is unclear if he was to take the flight to Utah, where the Knicks play Wednesday night.

Davis’ injury wasn’t the lone calamity that afflicted the Lakers, who were led by James’ 31 points, five rebounds and five assists.

Knicks big man Bobby Portis got a well-deserved ejection in the second quarter for a Flagrant Foul 2 — something the Knicks couldn’t afford because of Marcus Morris’ absence.

Portis took a wild swing at the head of a driving Pope, who was driving for an easy layup. If Portis was going for the ball, he missed by a mile, and James was furious, jabbering at Portis. Rajon Rondo did as well.

Afterward, Portis vehemently denied it was intentional and Knicks interim coach Mike Miller backed him up.

“I tried to block the ball, missed the ball, hit him in the head,’’ Portis said. “My apologies and I was happy to see him come back into the game. My intention was never to hit him in the head. I made a basketball play on the ball. My intent is to play hard. That’s my MO. I accidently hit him in the head.’’

Portis hit the showers and could be barred from the Knicks’ next game against Utah on Wednesday as the NBA reviews all Flagrant 2’s.

“I think it was not intentional,’’ Miller said. “I think he really was going for the ball.’’

Pope did not take his free throws and went to the locker room after spending time on the floor, wincing and touching his temples. He was examined for a concussion, but later cleared.

James was certifiably stoked. Despite being “under the weather” and missing the morning shootaround, he was a machine at night, firing sharp-angled passes, draining 3’s and rambling to the hole like a freight train.

But now James must wonder how long Davis may have to miss with this injury for the Lakers (30-7), who are now 21-0 against sub-.500 teams.

As for the Knicks, they fell to 10-27 — 6-9 under interim coach Mike Miller. They were led by RJ Barrett (19 points) and Randle (15 points).

The Lakers started the game with an easy alley-oop connection — Danny Green to Javale McGee. But the Knicks hung tough and were down just 26-21 after one quarter.

It was just a matter of time before the Lakers’ fast-paced game wore them out. The Lakers scored 21 fast-break points in the half and 30 in the game. Miller said that was the difference, though the Knicks shot just 38 percent.

With Morris out with a neck injury after scoring 38 points in this arena Sunday against the Clippers, Reggie Bullock, rather than Kevin Knox, started in his place and was just 1-of-5 from the 3-point line and finished with just 7 points. Knox continued to disintegrate, going 1-for-7 from the field.

Before the Davis fall, it got chippy in the third quarter when Bullock dragged down McGee, who had a layup attempt underneath. Bullock was charged with a Flagrant 1 after an angry McGee asked for a video review. Against the Clippers, the Knicks were flagged for four technical fouls.