Golden State beat visiting Utah 106-94 in the opener of their second-round series.
Thomas scored 20 points in the fourth quarter and nine more in a game-closing 15-2 over-time run that gave the host Celtics a 2-0 lead in the best-of-seven Eastern Conference series, which shifts to Washington for game three on Thursday.
Thomas attended his sister Chyna's funeral Saturday after she died in a car accident and has also had to overcome having had a tooth knocked out in a game-one victory Sunday.
"My sister, everything I do is for her, and she's watching over me," Thomas said.
On what would have been his sister's 23rd birthday, Thomas connected on 18-of-33 shots from the floor and 12-of-13 from the free throw line.
"The least I can do is go out there and play for her," Thomas said. "There was no way I couldn't play on her birthday. I wanted to win for her."
He did more than that, eclipsing his former career-best 52 points in a regular-season victory over Miami this season and his former playoff best of 42 last year against Atlanta.
In the Western Conference, NBA season wins leader Golden State beat visiting Utah 106-94 in the opener of their second-round series.
Celtics center Al Horford contributed 15 points and 12 rebounds while Jae Crowder and Avery Bradley each added 14 points for Boston.
But the only Celtics player to ever score more points in a playoff game was John Havlicek, who struck for 54 in 1973.
"It's nice (for) your name to be in Celtics' history with all the great players, but until you win one of them championships you can't call yourself a great player," Thomas said.
Thomas spent six hours with a dentist on Monday to repair his teeth and played with a custom-made dental guard.
"What else is there to say?" Celtics coach Brad Stevens said. "There was a point today where he was not feeling good at all. He's had a tough day and I thought he was going to really have to gut this one out.
"Not only guts it out, he ends up with 50. Pretty impressive."
John Wall led seven double-figure scorers for the Washington Wizards with 40 points and 13 assists, but 19 of those points and six assists came in the first quarter.
The Wizards, who led 42-29 after the first period, became the first team since the NBA introduced a shot clock in 1954 to lose the first two games of a playoff series after leading each by 10 or more points at the end of the first quarter.
"It was a hell of a basketball game," Wizards coach Scott Brooks said. "Two teams played their hearts out. Two great players played well. I thought both teams competed, nothing to be ashamed of."
Otto Porter's 3-pointer put Washington ahead 114-112 with 32 seconds to play in regulation but Thomas was fouled by Marcin Gortat and sank two free throws with 14.4 seconds remaining to pull Boston level again. Wall and Beal missed in the dying seconds to send the game into over-time.
In Oakland, California, Stephen Curry scored 22 points while Draymond Green and Kevin Durant each added 17 points and Klay Thompson had 15 as the Warriors showed no rust from a week off after a first-round sweep.
"Seven days can get a little bit tough," Green said. "We were a little beat up. It was good we got our guys healed up. We came out and showed good rhythm."
The Warriors scored the first nine points and would surge ahead 58-46 at half-time. Curry scored 16 first-half points while Durant and Thompson each added 10.
Utah stayed within 84-73 entering the fourth quarter, but the Warriors opened it with a 8-0 run as the Jazz missed their first six shots of the final period and Golden State pulled away to stay.
The Warriors were coached by assistant Mike Brown as Steve Kerr remained sidelined by complications following back surgery.