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Federer lifted his arms in jubilation, then leaned wearily on the net while awaiting congratulations from the big Argentine. They shared a warm embrace.

“I felt for him in a big way,” Federer said, “because I’ve been there as well.”

Said Del Potro: “It’s not an easy situation. Someone always has to win these matches, and today it was his turn.”

Del Potro will play Djokovic for the bronze Sunday.

The 6-foot-6-inch Argentine had the edge on Federer for most of the first two sets, reaching the net more often and winning most of the baseline rallies, starting with a 23-shot exchange in the opening game. Del Potro showed little effort as he snapped explosive forehands that had Federer scrambling and lunging.

“Not enough, Roger!” a British spectator shouted when Federer fell behind.

The near-capacity crowd on sunny Centre Court was clearly in Federer’s corner. Fans clapped and chanted “Ro-ger!” during a changeover, and later “Let’s go, Roger!” More than once a Swiss cowbell clanged.

Small clusters of Argentine fans broke into song, and the match — like the entire tournament — took on an atmosphere more festive than during Wimbledon.

Federer’s comeback came slowly. He was on the verge of digging a deeper hole midway through the second set, when he faced a break point and needed 16 points to hold for a 3-2 lead. He played another patchy game at 4-all, when he misplayed an overhead, blew an easy volley, squandered a 40-love lead and faced another break point.

He managed to hold again, and never trailed in the tiebreaker. Then the match proceeded on even terms for the next couple of hours.

In the 15th game of the final set, Del Potro twice won rallies after clipping the net cord with shots, the second time to erase a break point. Federer’s bad luck had him screaming in frustration.

But for the most part, he managed to keep any annoyance in check. In the 31st game of the final set, when he mishit back-to-back forehands — the second sailed long — he gave his wife a wry grin.

“I was very tense at certain times,” Federer said. “I was seeing myself as a loser many times during the match. But at the same time also I did see myself with medals. So you go through many emotions.”

Federer broke for the first time in the 19th game of the final set when Del Potro double-faulted twice. That gaveFederer a chance to serve for the victory at 10-9, but he was broken at love.

He waited 16 games for another chance, while repeatedly holding easily. Del Potro made three unforced errors in the 35th game to lose serve for only the second time, and eight points later the marathon reached the finish line.