The Celtics avenged a 117-116 loss to the 76ers in their opener at Boston and improved to 3-3 while dropping the host Sixers to 4-1.
"Just grit. I think we just slugged it out," said Brown, whose 13-of-19 shooting included 4-of-7 from three-point range.
"We made a bunch of mistakes, but we found a way to win in the end."
Tyrese Maxey, who led Philadelphia with 26 points and 14 assists, and VJ Edgecombe sank three-pointers to lift the 76ers within 108-106 with 51 seconds remaining.
Brown added what turned out to be the deciding free throw with 32.9 seconds remaining, but Maxey sank a layup with 20.8 to play to lift the 76ers within the final margin.
Brown, who scored 16 points in the first quarter, committed a foul to turn the ball over with 11.6 seconds remaining, but Maxey missed a short jumper.
After Boston's Josh Minott missed two free throws, the hosts had a final chance, but Joel Embiid, who had 20 points, missed a three-point shot at the buzzer.
Improving to 5-0 on the campaign were the Chicago Bulls, who were led by Josh Giddey's 32 points and 26 from Nikola Vucevic in a 135-125 home victory over the New York Knicks.
Jalen Brunson scored 29 points to lead the Knicks (2-3).
Chicago clung to a 120-116 lead when Vucevic went on a late 6-0 run and then assisted on a Giddey hoop to seal the victory.
Doncic scores 44 for Lakers, Jokic lands triple-double
Los Angeles Lakers star guard Luka Doncic, sidelined a week ago with a left finger sprain and lower left leg bruise, scored 44 points, grabbed 12 rebounds and passed off six assists in a triumphant return with a 117-112 victory at Memphis.
"I was very happy to see him back," Lakers standout Austin Reaves said.
"He has the capability of putting a team on his back, and I think he did that tonight."
Kawhi Leonard scored 34 points, including the game-winning basket with 0.4 of a second remaining, and James Harden added 24 to give the Los Angeles Clippers a 126-124 home victory over New Orleans.
Portland's Jerami Grant sank two free throws with 1.4 seconds to play to give the Trail Blazers a 109-107 home victory over Denver.
The Nuggets got 21 points, 14 rebounds and nine assists from Nikola Jokic, his streak of four straight triple-doubles to start the season ending in the defeat.
Devin Booker's 36 points led Phoenix to a 118-96 home victory over Utah.
The Atlanta Hawks, playing without star guard Trae Young due to a right knee sprain, improved to 3-3 by beating winless host Indiana 128-108.
Jalen Johnson led Atlanta with 22 points and 13 rebounds. The Pacers, who fell to 0-5, also learned Friday that forward Obi Toppin is out for three months due to a broken right foot.
Toronto had 20 points each from Brandon Ingram, RJ Barrett and reserve Jamison Battle in a 112-101 victory at Cleveland.
In the NBA Cup, all 30 NBA teams were drawn into six five-team groups, with each club playing four games through November 28th that will count in round-robin Cup play and the regular-season standings.
Eight teams will advance to the Cup quarter-finals: the six group winners and the top runner-up in the Eastern and Western Conferences.
Quarter-final matches will be played on December 9th to 10th, with the last four going to Las Vegas for semi-finals on December 13th and the championship game on December 16th.