MIAMI GARDENS, Fla. — It doesn’t happen often. It rarely happens on the main stadium court, at night, with two all-court players who serve hard but whom no one would describe as serve bots.

For nearly three hours at the Miami Open, Tommy Paul and Arthur Fils went after each other like two prize fighters, slugging it out from all over the court at Hard Rock Stadium. They played 36 service games. No one broke serve. They played three tiebreaks; the last one needed 2 extra points to decide the winner.

In the end, Fils, the 21-year-old Frenchman who has Jannik Sinner and Carlos Alcaraz had in his sights came out on top, a 6-7(3), 7-6(4), 7-6(6) winner of a duel that should take even the easygoing Paul a good while to recover from. Usually amiable in defeat, Paul skipped his media obligations, choosing instead to give some quotes to a Tour representative.

“He was able to close out the match when I wasn’t,” Paul said.

Paul saved a match point serving at 4-5 in the third set. Two games later, they went to tiebreak, and Paul painted the lines and surged out to a 6-2 lead with a series of charges to the front of the court.

Fils’ shoulders sagged as he netted a ball to put Paul on the brink. Fils looked finished. Really, he was just getting started.

At 2-6, Fils won a rally with a hard strike that Paul had to stretch to get a backhand on.

Paul served at 6-3, worked his way to the net, but popped a diving volley high as Fils cranked a desperation backhand at him, giving Fils an easy putaway. On the next point, Paul sent a forehand long to let Fils back on serve. Fils took it from there, a serve Paul couldn’t get back, and then a triumph in a backhand battle to make his first Masters semifinal.

“I just have to believe in myself, and that was the most important,” Fils said. “He was playing unbelievable, and you know, I just said, ‘OK, look, point by point, if I’m lucky, I get through it, otherwise it’s OK, it’s not a big deal. He was playing better than me, so. I just had to fight until the end, and we’ll see.”

He’d been downing pickle juice for the better part of the last hour. It worked.

“The legs are a bit hurting, they feel a bit tight, but you know when you win, usually you don’t feel it too much,” Fils said. “But if I have lost tonight, for sure tomorrow I couldn’t walk.”

Fils will face Jiří Lehečka of the Czech Republic in the semifinals Friday.