Tatum scored 33 points and Brown 28 as top seeds Boston, stunned by the Cavaliers on their home court in Game 2, beat the Cavs 106-93 in Cleveland to take a 2-1 lead in their best-of-seven Eastern Conference semi-final.
For Dallas, Irving scored 14 of his 22 points in the second half and Doncic scored 22 points and grabbed 15 rebounds as the Mavericks rallied for a 105-101 victory that put them up 2-1 against Western Conference top seeds Oklahoma City.
The Celtics emerged from a nip-and-tuck first quarter with a two-point lead and never trailed again.
"We just wanted to bounce back," Tatum said after they pushed their advantage to 23 points by opening the third quarter on a 14-0 scoring run.
"Essentially our back was against the wall, so it was a good test for us to see how we respond," Tatum said. "We were up for the challenge."
Donovan Mitchell scored 33 points for the Cavaliers, but appeared to tweak his troublesome left knee in the fourth quarter.
Cleveland halted Boston's third-quarter spurt with a 9-0 run of their own.
But the Celtics had an answer for every Cleveland surge and the Cavs could not get any closer than nine points behind in the final period.
Irving 'doing it all'
In Dallas, the Mavericks dug deep in the face of another bruising defensive effort from the Thunder.
Irving's second-half star turn included a floater that pushed the Dallas lead to five points with 39.3 seconds remaining.
Slovenian star Doncic took another pounding, including a hard fall flat on his back after a mid-air collision with Luguentz Dort, and said he tweaked his sprained right knee as the game ended.
"We got the win, that's all that matters," said Doncic, who when asked what was hurting the most - his knee, his back or his sore ankle - said "everything."
"I think I'm battling," he said. A day without travel before the Mavs host Game 4 on Monday was welcome, he added.
P.J. Washington led the Mavs with 27 points and Dereck Lively added 12 off the bench to help Dallas withstand a 31-point performance from Thunder star Shai Gilgeous-Alexander.
Both teams struggled to get their offences firing in the first quarter, which ended with Dallas up by three.
Oklahoma City connected on 60 per cent of their shots in the second quarter to take a 52-51 half-time lead and pushed their advantage to 65-55 with an 11-0 scoring burst in the third.
The Mavs responded with a 16-0 run that featured a huge dunk by Washington and was capped by his three-pointer that pushed their lead to 71-65.
The run energised the American Airlines Center crowd, but Oklahoma City quickly cut the lead to one before the Mavs responded again.
Irving connected on a pair of three-pointers and fed Daniel Gafford for a dunk before Tim Hardaway Jr. closed the third quarter with a three-pointer that put Dallas up 82-78.
Irving, who handed out seven assists as he focused early on getting his teammates involved, said one Dallas coach told him he'd left it a bit late to make a scoring push.
But Doncic said his contribution was "amazing."
"He's doing it all on both ends of the floor," Doncic said.
Thunder coach Mark Daigneault said his young team - with an average age of just over 23 - got a little sloppy in the third quarter to squander a golden chance to grab a win in Dallas.
"There's a lot of things we can learn from," he said.
