Brown recorded his first double-double in a half in his career with 18 points and 10 rebounds, while he added another 18 points in the third quarter.
The Celtics guard shot 15-of-21 from the field with three-of-six from three-point range along with 12 rebounds for the game.
Tatum went 10-of-22 from the field with 10 rebounds and four assists, with Malcolm Brogdon adding 20 points off the bench.
The game marked the seventh time this season that Brown and Tatum have scored at least 30 points each, which is joint for the most before February by two players from the same team in the last 40 seasons.
The result improves the Celtics to 30-12 overall and 17-5 at the TD Garden, while the Pelicans lose ground on the top two in the west, falling to 25-17.
C.J. McCollum scored 38 points for the Pels, marking the first time in his career he had 20-plus points in a first half in consecutive games.
Jokic falls short of triple-double as Nuggets triumph
Nikola Jokic fell one assist short of a 12th triple-double of the season as the Western Conference-leading Denver Nuggets claimed their fourth straight win, 126-97 over the Phoenix Suns.
The reigning back-to-back NBA MVP Jokic finished with 21 points, 18 rebounds and nine assists, including a brilliant first-quarter look-away fling to Aaron Gordon.
Jamal Murray added 16 points, although he picked up an ankle complaint, while Bones Hyland contributed 21 for the Nuggets, who have claimed 12 wins in a row at home, along with winning 14 of their past 17.
Grizzlies secure eighth straight win
Morant scored 21 points in the first half, finishing the game with 38 along with five rebounds and four assists.
The Grizzlies guard also produced a big dunk over Jakob Poeltl in the third quarter, while his put-back with 24.1 seconds left in the fourth sealed the victory.