Rondo had a triple double of 18 points, 10 rebounds and 10 assists to set up the showdown with LeBron James and Dwyane Wade's red-Hot Heat starting on Monday in Miami.
Eleven of Rondo's points, including a critical three-point shot, came after Celtics captain Paul Pierce fouled out with over five minutes to play and the game in the balance.
"My night wasn't going well. I just figured stay with it, stay positive, and something will happen," Rondo said.
Celtics coach Doc Rivers said Rondo displayed leadership, and shot-making, in the final minutes that is not always evident.
"Rondo wants to run the team, and he's a great quarterback. But tonight, obviously with Paul fouling out, he had to take charge of the team," said Rivers.
Center Kevin Garnett had 18 points and 13 rebounds for Boston, and forward Brandon Bass added 16.
Andre Iguodala top-scored for Philadelphia with 18 points while Elton Brand and Jrue Holiday each had 15 points.
But the Sixers shot only 35 percent from the field and made only 14 of 20 free throws in the team's first game seven since 2001.
"They hit us in the mouth early. We fought back, but we could never get over the top. We missed four of five free-throws (late in the third quarter) just when we were starting to get back into it," said Sixers coach Doug Collins.
Still, shaking off the Sixers was tough, said Rivers.
"The Sixers are a pain in the ass. They are a tough basketball team," Rivers added. "They are difficult to play against."
The series win means that Boston's "Big Three" veteran starters, Garnett, Pierce, and guard Ray Allen, will play together for at least one more series.
Allen turns 37 over the summer, while Garnett is 36 and Pierce is 34. Garnett and Allen will be free agents in the off-season, and many assume this will be their last season for Boston and possibly in the league.
The team's advanced age and creaky joints has forced a different approach to game preparation, Rivers said.
"We didn't practice one time in this entire series - that's unheard of ... we just don't have the bodies, we don't have the legs, to do anything else.
"But listen, we're not an excuse team. We'll be ready to play on Monday."