NEW ORLEANS -- In an early season filled with so many almosts, the New Orleans Pelicans finally got a chance Monday night to savor what it's like to make the critical, close-out plays that had eluded them during their woeful 1-9 start.

The result was a 106-105 victory over the Boston Celtics, the Pelicans' first home victory of the season after five losses at the Smoothie King Center.

Anthony Davis scored 25 points and guard Tim Frazier made a key steal on an inbounds play and canned two foul shots in the final 14.8 seconds to give the Pelicans the victory.

"It's not a monkey -- (it's) a gorilla, maybe," said New Orleans coach Alvin Gentry, referring to the mounting pressure created by the Pelicans' early-season struggles. "It's big. We have to win games at home. For us to hang on to win I think is really big. I'm not going to be one of those guys who says, 'Nah, it not (a big deal).' No, it's a big deal."

Trailing 103-102 with 33.1 seconds left, the Pelicans went to Davis, who missed a jumper in the lane but tracked down his own rebound -- his 16th of the game -- and was fouled. Davis made both free throws to put the Pelicans up 104-103 with 24.7 seconds left.

Davis got a piece of Avery Bradley's deep 3-pointer on the Celtics' next possession, but Boston controlled the ball when it went out of bounds in a rebound scrum.

When Marcus Smart tried to inbound the ball, Frazier sloughed off his man and picked off the pass that was intended for Amir Johnson. Frazier was fouled at 14.8 and made one of two foul shots, putting New Orleans up 105-103.

"It went so quick," Frazier said. "It was five seconds, and he had the ball out of bounds. I had switched on either Isaiah (Thomas) or Avery down low, and I just read Marcus' eyes. He threw it and I was able to jump in front of it."

After Thomas, who had a game-high 37 points, tied it at 105 with a left-handed layup, Frazier then pushed the ball up court quickly because the Pelicans had no timeouts.

Frazier was supposed to run a high pick-and-roll with Davis, but since he was ahead of the pack, he pump-faked Celtics center Kelly Olynyk about 20 feet from the basket and drew a shooting foul with 2.5 seconds left.

Frazier made one of two foul shots for the final margin of victory.

"He plays big," Davis said of the 6-foot-1 Frazier. "He went in there with all them trees down there and got that (interception). He had a great basketball IQ to draw that foul. That was a big play."

Olynyk said he tried to challenge Frazier's attempted shot but got caught in mid-air.

"He shot-faked and I tried to challenge it, a shot that I thought he was going to shoot," Olynyk said. "He jumped into me and I picked up the foul. It's really tough."

Boston coach Brad Stevens said he tried to focus his defense on stopping Davis' supporting cast, but New Orleans, for the first time in many games, got solid performances and balanced scoring.

Guard Langston Galloway had a season-high 21 points and forward Terrence Jones had 15 points and 10 rebounds, including three huge offensive rebounds that he converted into points.

"Jones has had great games against us for as long as I can remember playing against him," Stevens said. "Those other guys really hurt us tonight."

NOTES: Celtics C Al Horford, who sustained a concussion in practice more than two weeks ago, flew back to Boston before Monday night's game against the Pelicans to get ready for a full-go practice on Tuesday, Boston coach Brad Stevens said. "I don't want to put a timetable on it because I think it's all about how he feels day to day," Stevens said. "Once we made that decision (to not have Horford play Monday night), we actually got him a flight and got him home." ... The Pelicans are likely to get PG Jrue Holiday back this week, coach Alvin Gentry said. He missed all of training camp and the first month of the season caring for his wife Lauren, who gave birth to their first child and then underwent surgery to remove a benign brain tumor. "It's probably going to be within the week, for sure, maybe within a few days," Gentry said. ... With the Pelicans' victory, the Denver Nuggets are the only NBA team yet to win at home.