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And they’re now just one victory from an unlikely trip to the NBA Finals.

Finding a way to push past the Miami Heat’s season-long homecourt dominance, the Boston Celtics pushed past the league’s next generation of Big Three for a 94-90 victory over the Heat Tuesday night at AmericanAirlines Arena.

Paul Pierce helped put it away for the Celtics with a 3-pointer with 52.9 seconds to play, giving Boston a 3-2 series lead.

Kevin Garnett led the Celtics with 26 points and 11 rebounds, with Pierce adding 19 points and point guard Rajon Rondo 13 assists.

That proved to be enough to offset 30 points from Heat forward LeBron James and 27 from Heat guard Dwyane Wade.

The game marked the return of Heat forward Chris Bosh from a three-week absence with a lower-abdominal strain. He did not play the fourth quarter and finished with nine points and seven rebounds in 14 minutes, 23 seconds.

The Heat pushed to a six-point lead midway through the fourth quarter with a 9-0 run, but Boston then closed within 78-77 with 4:50 to play on a Rondo layup.

After a James layup was blocked by Garnett, Garnett hit a short jumper to push Boston to an 81-80 lead.

Heat guard Mario Chalmers then was called for a technical foul for a shove on Garnett, with a Ray Allen 3-pointer putting Boston up 82-80 with 2:54 to play.

From there, the Celtics worked for Pierce’s 3-pointer, which put Boston up 90-86, effectively ending it.

The Celtics tied it early in the third quarter, with the Heat’s smallish lineup, one that featured power forward Udonis Haslem starting at center, offering little resistance at the rim, as the Celtics loaded up on points in the paint.

But after a backcourt turnover from Rondo, the Heat then got a 3-pointer from forward Shane Battier, to take a 57-50 lead. A hook shot by Haslem extended the run to 9-0 and put the Heat up 59-50.

The Celtics, though, made another pushback, with a 3-pointer by guard Keyon Dooling just before the buzzer completing a 15-1 that gave them a 65-60 lead going into the fourth quarter.

The Heat went scoreless over the final 3:48 of the third quarter, unable to find shots in their halfcourt offense.

When Wade scored on a layup 30 seconds into the third quarter, it was his first points since 7:38 of the first period.

The Heat pushed to a 13-point lead early in the second quarter but saw the offense sputter when James went to the bench. After hitting his first three shots, Wade then missed his next six, returning to his recent first-half struggles.

With 11 first-half turnovers, the Heat gave away almost all of its early advantage, going into halftime up 42-40.

James led the Heat with 18 first-half points and nine first-half rebounds, with Brandon Bass pacing Boston with 20 points over the opening two periods.

After scoring 44 points in his previous visit, in the Celtics’ Game 2 overtime loss, Rondo missed his first six shots, not converting his first basket until 7:58 remained in the second period. Garnett also opened 1-for-6 from the field.

Rondo closed the first half with a sleeve on his left elbow after he was struck in the game.

It was an interesting first quarter on many levels, foremost because it featured the first action for Heat power forward Chris Bosh since May 13, when he sustained a lower abdominal strain in the first half of the first game of the Eastern Conference semifinals against the Indiana Pacers. Bosh entered with 5:06 left in the first quarter, his first appearance off the bench since Nov. 23, 2003, as a rookie with the Toronto Raptors.

With Bosh on the floor, contributing five quick points, the Heat pushed to an 11-point lead before taking a 24-16 edge into the second quarter. The Heat shot 10-for-19 in the first quarter compared to 6-for-20 for the Celtics, but Miami was limited by seven turnovers in the first period.

It was not the best of starts for Rondo, who shot 0-for-5 in the first quarter with just one assist. After struggling at the starts of previous games, Wade this time scored seven points in the first quarter.

NOTES: It proved to be a tumultuous 48 hours for Bosh, with a female masseuse dying at his home Monday. Police do not suspect foul play. “Our hearts go out to her family. We are very sorry for their loss,” Bosh and his wife, Adrienne, said in a statement issued before Tuesday’s game. …

The Heat opened with its third different center in as many game, with Udonis Haslem starting in the middle. Joel Anthony started for the Heat at center in Game 4, with Ronny Turiaf starting the first three games of the series. …

With Haslem starting, James jumped center for the Heat, winning the opening tip. …

Among those in the crowd was New York Knicks center Amare Stoudemire, who sat in the front row across from the Heat bench. …

Celtics coach Doc Rivers, on playoff life on the road, “I’ve always thought, at least for the second unit, the role players, it’s easier to play defense than it is to make shots on the road. You’re not as comfortable offensively.”