Davis, who moved into the starting lineup as Garnett was held out with a sore knee, had 19 points and matched his career high with 12 rebounds to lead the Celtics past the Atlanta Hawks 99-93 on Friday night.
Boston coach Doc Rivers said his team won with "mental toughness."
"We've got a group that believes they're going to win games no matter who's on the floor," Rivers said.
The big game by "Big Baby" Davis was frustrating for the Hawks, who could not take advantage of the absence of Garnett even while trying to play big with Zaza Pachulia starting on the front line with Al Horford.
"With their key guys out, they still have guys on the team who can get in there and play," Hawks coach Mike Woodson said. "Glen Davis was huge tonight, and we had nothing to stop him. I don't think that beat us, but the hustle in itself did. They banged a little harder than we did and they hustled a lot harder than we did."
Rivers held out Garnett, who's still experiencing soreness after missing 13 games with a right knee strain. Garnett played a limited role in four games after returning from the injury, but now could miss more time as Rivers attempts to have the high-scoring forward healthy for the playoffs.
The performance by Davis could help Rivers use patience with Garnett.
"Baby was physical," Rivers said. "He got his body in the way a lot. He's a big man and when he throws that body around, that's good for us."
Davis drew praise from others, but was critical of himself.
"Look at the stat sheet," Davis said. "I went 8-for-18. Out of 18 shots, I made eight. I'm my toughest critic. I had four turnovers. I had some bad fouls. I didn't execute at crucial times. I say that because I'm preparing myself for the playoffs."
The Hawks only saw Davis help the Celtics win almost every chase for loose balls.
"He was real active in the first half, and it carried over to the second half," Smith said, adding the loss to the Celtics was disappointing "with or without Garnett."
Rivers said Garnett, averaging 15.8 points and 8.5 rebounds was "just not feeling great," but would've been in uniform for a playoff game.
Atlanta took three home wins over the Celtics before falling in Game 7 in last year's first-round playoff series, but Boston has won three straight over the Hawks this season, including two at Philips Arena.
Boston twice led by 20 in the final quarter, the last time at 89-69 with 6:07 remaining.
"They just outplayed us for the first three quarters," said Atlanta's Josh Smith, who had 22 points and 11 rebounds. "It was embarrassing, to tell you the truth."
Flip Murray scored on a drive with 1:38 remaining to cut the lead to 93-88. Joe Johnson, who scored 22 points, hit a 3-pointer with 1:11 left to pull Atlanta within four at 95-91.
Pierce made four free throws in the final minute to protect the lead.
Woodson said the Hawks waited too late to start the comeback.
"We didn't play until the five-minute mark in the fourth quarter," Woodson said. "You can't beat a team like Boston when you don't start playing until then."
Mike Bibby added 19 points for Atlanta.
The Hawks, who have lost three of four, fell to the short-handed Celtics one game after a home loss to San Antonio, which played without Tim Duncan.
Boston led only 43-41 before pulling away with a 21-6 run that covered the final three minutes of the first half and the first five minutes of the second half.
Davis had a double-double in the first half with 10 points and 10 rebounds.
The Celtics stretched the lead to 17 points with a 12-5 run to open the second half. Rajon Rondo had seven points in the run.
Hawks coach Mike Woodson tried a big lineup, with 6-foot-11 Pachulia starting at center, pushing Horford to power forward. Pachulia had seven points and only two rebounds. Mo Evans, who had been starting for the injured Marvin Williams, moved back to a reserve role. ... Boston's bench outscored Atlanta's backups 25-17. ... After facing the Los Angeles Lakers on Sunday, the Hawks will have played the last four NBA finalists in a five-game span.