Latvian forward Kristaps Porzingis contributed 19 points, 10 rebounds, four blocked shots, three assists and two steals while Jaylen Brown added 17 points for the Celtics.
Jrue Holiday had 13 points, eight rebounds and seven assists for Boston, which avoided a first three-game losing streak this season after back-to-back losses in Atlanta.
"We want to be a hungry team no matter what," Porzingis said. "We haven't done anything and back-to-back losses to Atlanta is not in our DNA. It just didn't sit right with us, so we came out here tonight and got us a W."
The Celtics, who have clinched the Eastern Conference crown, improved to 58-16, moving closer to securing a home-court edge throughout the NBA play-offs.
New Orleans, fifth in the Western Conference, fell to 45-29, a half-game ahead of Dallas and two atop Phoenix in a fight for the last two guaranteed West play-off spots.
"We just knew we couldn't be in cruise control," Porzingis said. "These teams are hungry. They need these wins. Maybe we at this point of the season don't need them as much, but still we want to come out here and compete at a high level every night."
Porzingis was unhappy at shooting only 6-of-14 from the floor, and just 1-of-6 from 3-point range but pleased with his all-around effort.
"There are so many ways we can impact a game if things are not going perfect for us," Porzingis said. "That's what I did tonight. I turned up another notch and that's what we're going to need the rest of this regular season and then even more in the post-season."
Boston began the third quarter on a 15-7 run to open a 74-64 advantage on the way to an 83-68 lead entering the fourth quarter and the Celtics kept the Pelicans at bay over the final minutes.
"Once we hit another gear, the game just flipped," Porzingis said.
Derrick White, who scored 15 points, sank a 3-pointer at the second quarter buzzer to cap an 8-1 Celtics run for a 59-57 half-time Boston lead.
Tatum had 13 first-half points for Boston while Brown and Porzingis each scored 11.
Zion Williamson led New Orleans with a game-high 25 points, 12 in the first quarter, and nine rebounds while CJ McCollum added 24 points for the Pelicans.
Big night for Giannis
Milwaukee's Giannis Antetokounmpo scored 36 points, grabbed 16 rebounds and added seven assists, three steals and a blocked shot to spark the Bucks to a 122-113 victory in Atlanta.
The Bucks snapped the Hawks' four-game win streak - which included two wins over the Celtics - and improved to 47-27, stretching their lead over Cleveland for second in the East to two games.
Atlanta, led by Bogdan Bogdanovic's game-high 38 points, fell to 34-40, clinging to 10th in the East and the last play-in spot, a game behind Chicago.
Orlando's Wendell Carter had 15 points and 13 rebounds on a night when seven Magic players scored in double figures, none more than 15 points, in a 118-88 home victory over Memphis.
Orlando improved to 43-31, 1.5 games behind fourth-place New York in the East.
