NEW YORK -- With Kobe Bryant potentially playing his last game ever at Madison Square Garden, New York Knicks star forward Carmelo Anthony made sure to savor a spirited match-up with the player he affectionately calls his "big brother."

Anthony scored a game-high 24 points, including 11 in the fourth quarter, to help send the Knicks to a 99-95 victory over the Los Angeles Lakers on Sunday. Anthony spent much of the game in a physical battle with Bryant on both sides of the floor. Bryant finished with a team-high 18 points on 6-for-19 shooting in the game, which had the fans chanting "M-V-P!" for each of them at different times of the game.

"It kind of reminded me of back when I was on Denver and all those battles," Anthony said. "It always feels good to go up against him, my big brother. Even in his 20th season contemplating retirement, you still have to be on your toes going up against him. He's so smart of a player."

"Chasing 'Melo around, it felt really good," said Bryant, who echoed Anthony in calling it a brother relationship. "Bodying up and the physicality, it felt really good."

A late 3-pointer by Langston Galloway and tough defense in the final minutes made sure the Knicks (3-4) wrapped up their first home victory of the season and bounced back from a loss to Milwaukee. Galloway, a guard, nailed a 3-pointer from the wing with two minutes remaining for a two-point New York lead, and the never trailed again, coming up with four straight defensive stops after pulling ahead.

"The bigger plays were made on the defensive end," Knicks coach Derek Fisher said. "Offensively, our execution is still really an area we need to improve a lot, which we will do over time. It was really about the will to win and not lose the game, which was the most impactful."

"I think we just got bogged down mentally," Lakers coach Byron Scott said. "We stopped moving the ball like we did earlier. Everything was contested and the defense was right in front of us. I thought we really lost our focus."

Point guard Jose Calderon had one of his best games of the season with 14 points while controlling the tempo on offense, center Robin Lopez had 14 points, 13 rebounds and four assists, Galloway dropped in 14 points off the bench on 5-for-9 shooting and rookie forward Kristaps Porzingis registered his third double-double in his young career with 12 points and 10 rebounds.

"(Calderon) led us in the mental toughness department, and that was a big catalyst on why the guys found a way to win the game today," Fisher said. "A lot has been talked about on terms of if he should or should not be out there as a starter. Whether that ever changes, a big part of being successful in this league is being able to stare that type of conversation in the face and smile at people after he had a game like today, so I am happy for him."

Center Roy Hibbert added 18 points and nine rebounds in the loss for the Lakers (1-5). Second-year guard Jordan Clarkson chipped in with 10 points, and forward Julius Randle grabbed 11 rebounds.

Bryant's afternoon was no feel-good story for his former Lakers teammate, Knicks head coach Derek Fisher, who was ejected with 7:11 left in the third quarter. He was dismissed for arguing with the officials when Porzingis was whistled for fouling Bryant on a 3-point attempt.

Another former Laker, Kurt Rambis, took over for Fisher.

Bryant was then serenaded with chants of "M-V-P!" from the Garden crowd when he went to the foul line.

"(I'm) just appreciative of playing in such a historical building all these years," Bryant said. "I feel very, very fortunate to be able to have some of my best performances here in this building."

The Knicks recovered to take a 71-70 lead into the fourth quarter thanks to a go-ahead 3-pointer by Galloway.

The Lakers led by as many as eight points early in the third quarter when rookie point guard D'Angelo Russell, the No. 2 overall pick in this year's draft, dished out a pair of assists to Randle, but the Knicks answered with an 8-0 run following a timeout to tie it at 55.

The visitors grabbed a 49-45 halftime lead as Bryant led all scorers with 10 points on 4-for-11 shooting. Los Angeles held the Knicks to 34.7 percent shooting before the break, including a 3-for-9 showing by Anthony.

Bryant is used to having memorable nights on the road against the Knicks, as his 61-point explosion on Feb. 2, 2009, was the single-game scoring record at Madison Square Garden before Anthony erupted for a career-high 62 points against the visiting Charlotte Bobcats on Jan. 25, 2014. Bryant entered the afternoon with the highest scoring average at MSG of any active player at 30.7 points per game in 15 games.

NOTES: Lakers coach Byron Scott hinted that this may be G Kobe Bryant's final season, saying he asked Bryant about something next summer: "His answer was, 'This might be my last year,'" Scott said. ... Bryant shot down the idea of potentially becoming a coach after he retires: "I don't feel like dealing with divas." ... Knicks G Arron Afflalo missed his seventh straight game with a hamstring injury to start the season. ... Knicks F/C Kristaps Porzingis joined Patrick Ewing (1985), Jim Barnes (1964) and Willis Reed (1964) as the only rookies in Knicks history to put up at least 70 points and 50 rebounds through their first six games.