Boston's big three of Brown, Jayson Tatum and Al Horford combined for 87 points in a dazzling performance against a Suns team looking to avenge last Saturday's 117-107 home defeat to the Celtics in Arizona.
Tatum finished with 26 points while Horford weighed in with 24 to secure a victory that edges Boston closer to securing the NBA Eastern Conference's top seeding in the postseason.
The Celtics rained down a barrage of three-pointers on the Suns, converting 25-of-50 attempts from outside the arc. The Suns by contrast shot 11-of-31 from three-point range.
Devin Booker led the Suns scorers with 23 points, with Bradley Beal making 22 and Kevin Durant and Grayson Allen finishing with 20 apiece.
Celtics coach Joe Mazzulla saluted Brown's display.
"I think he's really taken the point of emphasis to being a well-rounded player," Mazzulla said.
"Everything with him starts with his defensive intensity. Getting off to a great start defensively gets him going and that's big for our team.
"And he can score on anybody at any time. He's playing really well-rounded basketball on both ends. It's fun to watch."
Thunder back on top
Boston improved to 52-14 and are 9.5 games clear of second-placed Milwaukee (43-24) at the top of the Eastern Conference.
Phoenix fell to 38-28 and are seventh in the Western Conference, outside the top six automatic play-off places.
Suns coach Frank Vogel admitted his team were not at Boston's level - but insisted there was plenty of time for improvement with the start of the postseason looming in April.
"We're just not quite where they are yet," Vogel said. "But that's the key word - yet.
"We're going to keep growing, we're going to keep getting better. We're in our first year together. Those guys (Boston) have been together eight years or something."
In other games, the Oklahoma City Thunder returned to the top of the Western Conference - just - with a 126-119 win over the Dallas Mavericks.
With Luka Doncic missing after suffering a tight hamstring in Wednesday's win over Golden State, Kyrie Irving led the Dallas challenge with a game-high 36 points.
But Oklahoma City pulled away in the second half to seal victory thanks to 31 points from Shai Gilgeous-Alexander and 27 from Jalen Williams.
The win leaves Oklahoma City in top spot in the Western Conference, level with NBA champions Denver on 46-20.
Oklahoma City are in first place by virtue of their 3-1 record against Denver in meetings this season.
Elsewhere, the Milwaukee Bucks produced a fourth-quarter rally to defeat the Philadelphia 76ers 114-105.
The Sixers, still without injured NBA Most Valuable Player Joel Embiid, led by 10 early in the third quarter but were gradually reeled in by the home side.
Giannis Antetokounmpo led the Milwaukee scoring with 32 points, with Brook Lopez adding 19 and Damian Lillard 17.
Tyrese Maxey shouldered the Sixers' offensive burden with 30 points including 5-of-9 from three-point distance.
The win continued Milwaukee coach Doc Rivers' perfect record against his former clubs since joining the Bucks in January.
The Los Angeles Clippers closed the gap on Denver and Oklahoma City with a comfortable 126-111 road win over the Chicago Bulls.
Chicago led briefly early in the first quarter but the Clippers took over and led for the remainder of the game, opening up a 21-point advantage towards the end of the fourth quarter.
Paul George finished with 28 points, including 6-of-7 from three-point distance, while Kawhi Leonard added 27.
The Clippers improved to 42-23 to remain fourth in the West, 3.5 wins behind Denver and Oklahoma City (46-20).
