After a shaky first week, the stumbles of Rafael Nadal and Roger Federer suddenly smoothed Saturday. Each turned in his most convincing performance of the tournament, buoying hopes that they might finally face off at the United States Open for the first time in their careers.

For Nadal, his tournament may have flipped on a single point.

Midway through the second set of his third-round match against Leonardo Mayer, Nadal failed to convert 13 break-point chances. Many were saved by strong serves that Nadal could not return.

But on the 14th chance, 1 hour 56 minutes into the match, Nadal’s forehand return drew an error from Mayer’s forehand to secure a break for a 4-3 lead in the second set. He pumped his arms four times and pounded on his chest twice as the crowd roared.

The din broke the tension: Nadal would break Mayer five more times, winning 14 of the next 16 games to put the match out of reach, ultimately winning, 6-7 (3), 6-3, 6-1, 6-4, in 3 hours 15 minutes.