NEW ORLEANS

Anthony Davis was nearly too ill to suit up.

Instead, New Orleans’ first overall draft choice sent the Boston Celtics out of the Big Easy with the sick feeling that accompanies a lost lead in the dying seconds.

Davis outreached Kevin Garnett and Jeff Green for a last-second tip-in, and the Hornets snapped a four-game skid with an 87-86 victory over the Celtics on Wednesday night.

“His first game-winner comes on night when he’s sick and puking and doesn’t feel his best,” Hornets coach Monty Williams said. “So kudos to him.”

Davis had missed the morning shootaround with an upset stomach. He was listed as a game-time decision and wound up with nine points, eight rebounds and two blocked shots in 28 minutes.

Ryan Anderson scored 21 points and Eric Gordon 18 for the Hornets. Gordon’s floater to win it in the waning seconds missed, but Davis followed up for the winner.

“I was really tired, but I knew my team needed me, so I was trying to fight through it,” Davis said. “I’m glad I did. It was a big win for us.”

Paul Pierce scored 11 of his 28 points in the last six minutes to nearly lead Boston back from a nine-point deficit, but missed a jumper with 16 seconds left that could have put the Celtics up by three.

Garnett returns

Garnett, returning from a two game absence caused by a left thigh injury and the flu, scored 20 points to go with six rebounds, but took the blame after Boston’s second-straight loss for not picking Davis up in time.

“It was my block-out. I was trying to help Avery (Bradley)” defend Gordon’s drive, Garnett said. “That’s just when you’re trying to help a teammate and you’re reacting. … I’m acting off impulse as a big man to try to block shots and protect the basket and (Davis) took advantage.”

Davis said he was unaware of who stood in his way for the winning tip.

“I was just following like I was supposed to,” Davis said. “I just saw the ball. I wasn’t looking at nobody else.”

The Celtics got the ball back one last time with 0.3 on the clock, and Pierce inbounded to Garnett, who could not get off a turnaround jumper before the horn.

The loss dropped Boston into seventh in the Eastern Conference, 3 1/2 games behind Brooklyn for the fourth seed, which carries with it home advantage in the first round of the playoffs. The Nets beat Dallas, while fifth-place Atlanta beat Milwaukee to pull 1 1/2 games ahead of the Celtics.

Boston coach Doc Rivers said the Celtics got what they deserved, adding that he could see it coming late in the second quarter when Boston “went from being a solid, good-looking team to show time.”

“We started dancing around, stopped defending. You could see our guys laughing and joking,” Rivers said. “We don’t learn because we have done this three or four times this year.”

Green, coming off a careerhigh 43 points in Boston’s loss to Miami on Monday night, scored 13 points, all in the first half.

Boston had been in control much of the game and led by as many as 13 after Pierce’s 3 made it 60-47 early in the third quarter.

Then Boston slumped offensively, scoring only 12 in the period, and New Orleans whittled away.

The Hornets went on a 9-2 run that included dunks by Robin Lopez and Al-Farouq Aminu, and tied the game at 65 on Anderson’s free throws late in period.

Boston led by as many as 12 in the opening half, taking a 50-38 lead on Garnett’s layup, and the Celtics led 55-45 at halftime.

Notes: While Austin Rivers’ broken right hand prevented him from playing against the team his father coaches, the younger Rivers said he was able to take his father out for dinner at one of celebrity chef Emeril Lagasse’s New Orleans restaurants on Tuesday. “That’s the first time I’ve ever paid for my dad,” Austin Rivers said. “The bill came and I was ready to get up. He looked at me like, ‘It’s your turn now.’ It feels good. “