"I wasn't really paying attention. I was just playing," Davis said when asked if he realized it was his highest-scoring night. "A career high. Whoop-de-do. I hope I get another one soon."
Garnett, still playing limited minutes in his second game back from a right knee injury, scored 10 points and grabbed four rebounds in 17 minutes.
"He clearly could have played more, and he was a little frustrated when we took him out," Celtics coach Doc Rivers said. "I had to call a timeout just to get the clock to stop."
Pierce, Boston's leading scorer with 20.5 points per game, was limited to six on 2-of-6 shooting.
"Offensively, we're going to our second and third options when teams take us out of our first option," said Boston guard Rajon Rondo, who scored nine points and handed out 10 assists.
Hakim Warrick scored 20 points for Memphis, which dropped its sixth straight at home and fourth in a row overall. Rudy Gay finished with 15 points on just 5-of-15 shooting, while O.J. Mayo and Mike Conley scored 12 apiece.
The Celtics broke open a close game at halftime by outscoring Memphis 26-17 in the third quarter. Then Boston opened the fourth quarter with a 14-4 run to lead by 23. At that point, Allen, Pierce and Garnett were done for the night, and the reserves played out the final quarter.
Memphis was able to stay close in the first half, despite Boston shooting better than 50 percent in the early going. In fact, both teams were making better than half their shots by intermission, the Celtics shooting 53 percent, while the Grizzlies were at 51 percent.
Memphis was getting its points inside, holding a 24-14 advantage in the paint, while Boston was doing its damage from long range, connecting on six of its 11 shots from outside the arc.
Davis got untracked off the Boston bench, hitting five of his seven shots and going 5-of-6 on free throws for 15 points in the half, while Allen added 13.
"Teams don't look at me as a serious option," Davis said. "But the more I get experience, and the more and more I get put in game situations, it will happen."
Neither team led by more than five, and there were 11 ties and 16 lead changes in the first half alone.
The second half would not be near that close, as Memphis shot 30 percent, including 25 percent in the fourth.
"The urgency rose in the third quarter," Rivers said. "We just traded baskets with them in the first half. Our offense played good, but we just didn't have much energy on either end of the first half."
The Celtics eventually got some breathing room in the third when consecutive jumpers from the left baseline by Garnett gave Boston its first double-digit lead of the night at 70-59. Kendrick Perkins' 5-footer capped 10 consecutive points for the Celtics.
"When Garnett was on the court at the start of the third quarter, they really had a lot of energy. Their defense was good. We couldn't really run anything," Memphis coach Lionel Hollins said. "I think they had a mind-set that they were going to try and increase their lead while Garnett was on the court."
After the rally, Garnett, who is playing about 7 minutes per half while recovering from the right knee strain, was on the bench. But the Celtics maintained the lead, carrying a 78-65 advantage into the fourth.
"We played them pretty good up until the third quarter," Gay said. "We need to learn how to withstand their runs and come with our own."
Rivers said before the game that he will try to extend Garnett's minutes on Monday night against the Clippers. Garnett, who played 15 minutes on Friday night, logged 17 minutes against the Grizzlies. Allen missed the second of two free throws with 2:41 left in the third, breaking a string of 57 straight. Allen has made 129 of his last 131 from the line. House entered the game shooting 56 percent (60-of-108) from outside the arc over the last 27 games. He went 4-of-9 against the Grizzlies. The game was a sellout (18,119), only the second of the season for the Grizzlies. The other was when the Los Angeles Lakers came to town on Jan. 31. ... Davis' previous high was 20 against Detroit on Jan. 5, 2008.