Tatum added 13 rebounds five assists and a couple of steals and the Celtics' suffocating defense neutralized newly minted NBA Most Valuable Player Joel Embiid as Boston booked a return date with the Miami Heat -- the team they beat in seven games in last year's conference finals.
Jaylen Brown added 25 points for Boston, who broke open a close game in the third quarter as they out-scored the 76ers 33-10.
Philadelphia went six minutes of the period without a basket and trailed by 26 heading into the fourth, when Boston pushed the lead to 30 with less than four minutes to play.
His 51 points eclipsed the game-seven record of 50 set by Golden State's Stephen Curry against the Sacramento Kings in the first round this month.
It was a bounce-back performance for Tatum, who struggled for long stretches in the series and endured a horrific shooting night until drilling four crucial three-pointers in the fourth quarter of the Celtics' series-extending game-six win on Thursday.
He began fashioning his game-seven masterpiece in the opening minutes.
The 76ers turned an early six-point deficit into a 29-23 lead through one quarter, while a nip-and-tuck second period saw the Celtics up 55-52 at halftime.
Then the Celtics blew it wide open in the third. Tatum scored 17 points in the period, draining four of his six three-pointers as the shell-shocked 76ers struggled, and failed, to find a response.
"Going into game six I was too locked-in, I was too tight, thinking about what I need to do, how many points I need to score," Tatum said.