Brown took an accidental elbow from teammate Jayson Tatum as they both went for a rebound with less than two minutes left in the first half and was knocked out of the game with a facial contusion.
It was a potentially crushing blow for a Celtics team already without Marcus Smart, Robert Williams and Al Horford, but the Eastern Conference leaders didn't miss a beat.
"Tonight was the definition of a team win," Tatum told broadcaster ESPN after the Celtics shot 52.6 percent from the floor, draining 19 of their 35 three-point attempts.
Tatum himself had a quiet night with just 12 points, eight rebounds and nine assists, connecting on just five of his 15 shots from the field.
But his unheralded teammates did more than enough to hold off the Sixers and their MVP candidate Joel Embiid, who led all scorers with 28 points.
James Harden scored 20 for Philadelphia, who never led after the first quarter.
Down by 11 with 5:51 to play, the 76ers would twice cut the deficit to three, but the Celtics found the answers.
Derrick White and Malcolm Brogdon scored 19 apiece for Boston. Blake Griffin drained five three-pointers while Sam Hauser and Grant Williams hit four apiece.
"Those guys are putting in so much work," Tatum said of the players who stepped up. "And they're professionals. When they get their number called they come in and compete."
The Cleveland Cavaliers also shook off notable absences in a wire-to-wire 113-85 home victory over the Detroit Pistons.
Jarrett Allen scored 20 points, Evan Mobley added 19 to lead the Cavs, who were without All-Star starter Donovan Mitchell and Darius Garland, Mitchell sitting out to rest a nagging groin injury and Garland out with a troublesome thumb.
The Cavs led by 18 after the first quarter on the way to a fourth straight victory.
The Pistons sliced the deficit to two points in the third quarter, but Cleveland outscored Detroit 37-17 in the final period as the Pistons were held to their lowest points total of the season.
Kings edge Rockets
The Sacramento Kings edged the Rockets 130-128 in Houston, where De'Aaron Fox made three free throws with three-tenths of a second left to seal it after Eric Gordon was charged with a debatable shooting foul.
Fox scored 13 of his 31 points in the fourth quarter as the Kings withstood 41 points from Houston's Jalen Green to win a tight back-and-forth battle that featured 22 lead changes.
In Toronto, Pascal Siakam scored 37 points and pulled down 10 rebounds to lead the Raptors to a third straight victory, 112-98 over the reeling San Antonio Spurs.
Siakam notched his fourth 30-point double-double of the season and 22nd of his career. He connected on all seven of his attempts in the first quarter on the way to 18 points -- his season high for a single period.
The Miami Heat enjoyed a return home after a disappointing 1-3 road trip, beating the Indiana Pacers 116-111.
Bam Adebayo scored 38 points and Jimmy Butler added 25 as the Heat stretched their season-best home win streak to seven games.