MIAMI — This was more exhale than exultation.

The hope is that will follow.

For now, there is the mere satisfaction of traversing the long road back to the NBA Finals.

With the hope for a better result.

A year after falling two games short of the franchise's second NBA championship, the Miami Heat will get its shot at redemption, with Saturday night's compelling 101-88 Game 7 victory at AmericanAirlines Arena finally finishing off the Boston Celtics.

"We wanted to give our fans a big win," LeBron James said after leading the Heat with 31 points. "We look forward to the next challenge."

While a modest Eastern Conference championship celebration followed, this has never been about something as mundane, something James, Dwyane Wade and Chris Bosh achieved last season, in their first together as teammates. This, instead, has, from the moment the NBA lockout ended in December, been about pushing past the sting of last year's Finals failure against the Dallas Mavericks, with Nowitzki, Terry, Kidd and Cuban exulting on the Heat's home court and then in the clubs of South Beach.

But Saturday was playoff theater at its finest, with Bosh stepping back to hit three-pointers, James attacking the basket for three-point plays, Wade again coming on strong in the second half and the Heat finally surviving.

"That's what we talk about," James said. "It has to be a collective group to win the championship. Everybody was in tune today."

In a game that featured 20 lead changes and 10 ties, with the Heat never up by more than two through the first three quarters, James, Bosh and Wade finally put it away late.

"They're really talented," Celtics coach Doc Rivers said. "Erik [Spoelstra] does a terrific job. I wish he got more credit with what he does with that group."

Wade scored 23 points for the Heat and Bosh, who converted a career-high three three-pointers, contributed 19.

"He was the X-factor," Rivers said of Bosh. "He gave them exactly what they needed."

For the Celtics, who now face a major post-Big Four overhaul, with Ray Allen and Kevin Garnett to be free agents, Rajon Rondo again was magnificent, with 22 points, 14 assists and 10 rebounds. Paul Pierce, who again fought foul trouble, had 19 points, Garnett 14 and Allen 15.

"I just thought we had nothing left," Rivers said. "That's how it felt as a coach."

The second finals of the Heat's Big Three era comes after challenges far greater than the path taken in 2011. This time there was the revival of the rivalry with the New York Knicks in the first round, the 2-2 uncertainty against the bulkier and bigger Indiana Pacers in the second round, and then this latest test against a Big Three that eventually reached its expiration date.

"I guess that's what a seven-game Eastern Conference series is supposed to be like," Spoelstra said. "It was good to see us come together in a very competitive series.

"We've been through a lot in two years."

Instead of the Heat reconsidering its own Big Three as well as the fate of Spoelstra, those questions, at least for now, are put aside in favor of the challenge of the Oklahoma City Thunder, in a best-of-seven NBA Finals series that opens Tuesday at Chesapeake Energy Arena. The Finals will be a 2-3-2 format

Rondo, Garnett, Allen and Pierce have now been vanquished by the Heat for a second consecutive season.

Ultimately, it again was James pushing the Heat to the finish line.

"He was absolutely brilliant this series," Spoelstra said. "And we all know it. He's playing at a historic level in these playoffs.

"He is pushing himself beyond his limits. And he's pushing the rest of the team, as well."