His tally of 70 points beat the franchise record of 68, held by the legendary Wilt Chamberlain since 1967.
Embiid also made a career-high 18 rebounds and contributed five assists.
“When he gets motivated like that, anything can happen,” said 76ers coach Nick Nurse.
“He can score in so many ways. His sheer size gets him a lot of stuff around the basket and a lot of free throws.
“And his shooting touch is the skill that makes it extra hard to stop him.”
Tyrese Maxey was the next highest scorer for the 76ers with 18 points, while number one draft pick Victor Wembanyama scored 33 for the Spurs.
The 76ers, who have won three successive games, are third in the Eastern Conference, while the Spurs are bottom of the Western Conference with only eight wins from 43 matches.
Karl-Anthony Towns scored a franchise record 62 points in the Minnesota Timberwolves’ 128-125 home defeat by the Charlotte Hornets.
It was only the fourth time – and the first since 1978 – when two NBA players scored at least 60 points on the same day.
When Embiid, the NBA’s Most Valuable Player, broke the 76ers record with one minute 41 seconds remaining, they called a timeout to allow him to leave the game. He received a standing ovation at the Wells Fargo Center in Philadelphia.
David Robinson, David Thompson, Elgin Baylor, Kobe Bryant, Donovan Mitchell, Devin Booker and Damian Lillard are the other players to score 70 points or more in a game.
Chamberlain holds the record with 100 for the Philadelphia Warriors against the New York Knicks in 1962.
The game was played 18 years to the day since Los Angeles Lakers legend Bryant scored 81 points against the Toronto Raptors – the second-highest individual haul in NBA history.
“From the time I started playing, Kobe was my guy,” Embiid said.
“He’s the reason I started playing basketball. It’s funny, on the same night he got 81 and was my favourite player.”
Embiid has now scored at least 30 points in 21 consecutive games.
Kevin Durant scored a season-high 43 points to help the Phoenix Suns to a 115-113 home win over the Chicago Bulls.
Giannis Antetokounmpo scored 31 points and made 17 rebounds and 10 assists to help the Milwaukee Bucks to a 122-113 victory - their ninth in succession - at the Detroit Pistons.
Jayson Tatum contributed 39 points and 11 rebounds as the Boston Celtics won 119-110 at the Dallas Mavericks, for whom Luka Doncic scored 33 points.