Brown scored 36 points and Tatum 33, Kristaps Porzingis adding 15 on his return to Washington after an off-season move between the clubs.
It is the second successive season the Celtics, who reached the Eastern Conference finals last time out, have begun with three straight wins.
Their efforts were eclipsed by Dejounte Murray, who matched his career-best haul with 41 points as he helped the Atlanta Hawks come from 19 points down at half-time to beat the Minnesota Timberwolves 127-113.
Steph Curry shrugged off the absence of Klay Thompson with a knee injury as he inspired the Golden State Warriors to a 130-102 win at the New Orleans Pelicans.
Curry scored 42 points, opening with a pair of three-pointers from 25 feet and wrapping his scoring up from 31 feet.
The Dallas Mavericks remain unbeaten as Luka Doncic grabbed a triple-double with 35 points, 12 rebounds and 12 assists in a 125-110 win over the Memphis Grizzlies.
Nikola Jokic also recorded a triple-double – his second of the season – with 27 points, 11 assists and 10 rebounds as the Denver Nuggets saw off the Utah Jazz 110-102.
Giannis Antetokounmpo scored 33 points for the Milwaukee Bucks as they avenged being eliminated by the Miami Heat in last year’s play-offs with a 122-114 win, despite 35 points from Tyler Herro.
Cam Thomas scored 33 points as the Brooklyn Nets beat the Charlotte Hornets 133-121 for their first win of the season, while Nikola Vucevic inspired the Chicago Bulls as they came from behind late to inflict a first defeat on the Indiana Pacers, 112-105.
The Portland Trail Blazers also claimed their first win, Jerami Grant scoring 22 points as they beat the Toronto Raptors 99-91, while 32 points from Shai Gilgeous-Alexander lifted the Oklahoma City Thunder past the Detroit Pistons.
Julius Randle had 27 points and 10 rebounds and RJ Barrett added 26 points in his return from injury as the Knicks handed the star-studded Clippers their second straight defeat following a 3-1 start to the season.
Harden took the court for the first time since being traded to Los Angeles by the Philadelphia 76ers last week. The 10-time All-Star had 17 points on 6-of-9 shooting along with six assists as a part of a starting lineup that included three other accomplished veterans in Kawhi Leonard, Paul George and Russell Westbrook.
The dynamic guard scored five straight points late in the third quarter to give the Clippers a 76-73 lead, but the Knicks countered with a 16-3 run to take an 89-79 advantage with under 9 1/2 minutes left and never trailed thereafter.
Barrett scored 11 points in the fourth quarter after missing New York's previous two games with a sore left knee, while Mitchell Robinson finished with 13 points and 15 rebounds to help the Knicks snap a two-game losing streak.
Edwards sparks overtime win as Wolves hand Celtics first loss
Anthony Edwards scored eight of his 38 points in overtime as the Minnesota TImberwolves handed the Boston Celtics their first loss of the season with a 114-109 victory.
Edwards added nine rebounds and seven assists to help Minnesota overcome an off night from fellow star player Karl-Anthony Towns, who managed just seven points in 28 minutes before fouling out in overtime.
Jaden McDaniels hit a game-tying 3-pointer late in regulation and finished with 20 points for Minnesota, which also received 14 points and 12 rebounds from Rudy Gobert en route to its third straight win.
Boston entered the game as the NBA's lone remaining unbeaten team following a 5-0 start. The Celtics got 32 points and five steals from Jayson Tatum and 26 points from Jaylen Brown, but shot just 28.2 per cent from 3-point range as well as a season-low 39.1 per cent overall.
The Celtics held a 105-103 lead after Tatum hit two free throws with 3:56 left in overtime, but Minnesota's Mike Conley buried a 3-pointer on the ensuing possession before Edwards capped a pivotal 9-0 run with three consecutive baskets that put the Timberwolves up for good at 112-105 with 1:30 remaining in the extra session.
Adebayo's triple-double propels Heat past Lakers
Bam Adebayo delivered a massive performance with 22 points, 20 rebounds and 10 assists, and the Miami Heat overcame a late scoring drought to hold on for a 108-107 win over the Los Angeles Lakers.
Adebayo became the first Heat player to record a triple-double with at least 20 rebounds, and Miami received 28 points from Jimmy Butler and 22 from Tyler Herro to record its second straight win following a four-game losing streak.
The Heat prevailed despite nearly blowing a 10-point lead with four minutes to play and not making a field goal over the final 4:15 of the contest.
The Lakers scored the game's final nine points and had a chance to win in the final seconds, but Cam Reddish was off the mark with a jumper and Butler grabbed the rebound right before time expired.
LeBron James finished with 30 points on 13-of-23 points to pace the Lakers, while Austin Reaves just missed a triple-double after compiling 23 points, 10 rebounds and nine assists.
Los Angeles has now dropped the first two outings of its current four-game road trip and played the entire fourth quarter without star forward Anthony Davis, who sustained a groin spasm during the game and was limited to nine points in 25 minutes.
