The 25-year-old scored 21 points in the fourth quarter alone and totaled 11 rebounds and four assists in an impressive performance.
The Celtics had been 14 points down with just over four minutes to play in regulation time but rallied back with Brown putting his side ahead 100-98 with just 30 seconds remaining.
Orlando’s Tim Frazier scored to force overtime before Boston pulled away in OT.
“Faith, consistency, hard work pays off,” Brown said after the game. “My teammates found me tonight and I knocked some shots down.”
Brown, who became just the seventh player in the franchise’s history to reach 50 points in a regular-season game, said he wasn’t fully aware of his tally until the final moments.
“To be honest, I didn’t even realize until the last shot when I had 47,” he added. “I was just being aggressive, getting to the basket.
“I didn’t feel like those guys could stay in front of me, so I was just going to keep getting to the basket, blowing by them on the first step, and I looked up and I had 47.”
Both teams had gone into Sunday’s game without their leading scorers.
Orlando’s Cole Anthony is sidelined with a sprained ankle while Celtics forward Jayson Tatum is out due to Covid-19 concerns.
Fortunately for Boston, Brown was there to fill the void.
“The growth with JB [Brown] is very real. I think we’ve all witnessed it,” said teammate Marcus Smart.
“He’s going to continue to get better, and the growth is going to continue to grow, and for this team, we need that.”