Tatum, who had just 31 points on nine-of-32 shooting in the first two games of the series, shot a blistering 16-of-30 from the floor and drained five threes as the Celtics cut the Nets series lead to 2-1.
Tatum also scored 50 points in a win over Washington in a play-in game making it the second time this month he has put the team on his back for a much needed post-season win.
"I just tried to be better," said Tatum. "I had a tough two games so I tried to redeem myself and do anything I can to win."
The Celtics' win over the Nets played out in front of a crowd of 4,700 at the Boston Garden.
"It felt good to finally play a playoff game at TD Garden and it is great being back in front of our fans," said Tatum.
Game four is Sunday in Boston.
Marcus Smart scored 22 points and Tristan Thompson finished with 19 points and 13 rebounds in the win.
James Harden delivered 41 points and 10 assists while Kevin Durant finished with 39 points and nine rebounds for the Nets, who were trying to take a 3-0 series lead for the first time since their first-round sweep of the New York Knicks in 2004.
Kyrie Irving was playing in front of Boston fans for the first time since leaving the Celtics under a cloud of controversy after the 2018-19 season.
He was showered with boos from Celtic faithful every time he touched the ball.
Irving scored just two points in the first half to tie a career low in a playoff game. He finished with 16 points on six-of-17 shooting.
The Celtics led 33-32 at the end of the first and 61-57 at the half, then held on down the stretch as Tatum nailed a clutch pull up jumper with 40 seconds left to make it 122-115.
"It's just one of those nights." Tatum said. "A tough shooting night the first game and I didn't get to play much the last game because I got poked in the eye."
His jumper came just 18 seconds after Irving had sunk two free throws to cut the Boston lead to five points.
Tatum joined John Havlicek, Isaiah Thomas, Ray Allen, Sam Jones and Bob Cousy as Celtics with 50 points in a playoff game.
- Irving booed -
"He was just locked in mentally," teammate Marcus Smart said. "We're going up against a juggernaut of a team."
Also, Trae Young scored 21 points and had 14 assists as the Atlanta Hawks beat the New York Knicks 105-94 to grab a 2-1 lead in their Eastern Conference first-round series.
The Hawks shot a sizzling 59 percent from the three point line and took command with a 22-5 burst to close out the second quarter.
Game four is Sunday in Atlanta.
Bogdan Bogdanovic scored 15 points, John Collins added 14, Clint Capela finished with 13 points and 12 rebounds. Former Knick Danilo Gallinari sank all four of his three-point attempts to finish with 12 points in the win.
Derrick Rose shot 13 of 21 from the floor and scored 11 of his 30 points in the first quarter for the Knicks. Julius Randle finished with 14 points in the loss.
Elsewhere, Kawhi Leonard scored 36 points and the Los Angeles Clippers rallied from a first half deficit to beat the Dallas Mavericks 118-108 in game three of their playoff series. The Mavericks lead the best-of-seven series 2-1 heading into game three on Sunday.