The 32-year-old Australian, a former No. 1 now ranked 66th after a series of injuries, repeatedly scrambled along the baseline to come up with passing winners against the sixth-seeded del Potro.
"I don't know how many years I've got left in me. I keep getting asked the question," said Hewitt, who won Wimbledon in 2002. "I'm just pumped to get out on this court and try to put on a great show."
Murray too looked like he might fall victim to a persistent opponent when Mayer snatched the third set, but the Scot was able to steady and quickly get through the fourth for victory.
"He's a big hitter of the ball. I had to defend a lot," Murray said in an on-court interview. "He played some really, really good tennis. It made for an entertaining match."
Becker had a chance to serve for the first set against Djokovic at 5-4. But he wasted the first set point with a forehand into the net and the second when a backhand sailed wide.
"Becker is a quality opponent and he should have won the first set," Djokovic said. "I was fortunate enough to come back and win the first set, and after that, I was much more comfortable on the court."
Djokovic was playing in Arthur Ashe Stadium, where the wind often swirls to players' frustration.
"You need to have this adjustment, footwork, steps, in order to get on the ball," Djokovic said. "I didn't have that in the first set. I was still trying to find my way from baseline, and the other side he was serving well. ... After I played a good tiebreak, everything kind of settled. I started to serve better, started to step into the court, which is important."
In the women's draw, defending champion and top seed Serena Williams had a predictably comfortable 6-3, 6-1 win over Yaroslava Shvedova of Kazakhstan.
That set up a fourth-round clash with American compatriot Sloane Stephens, who produced one of the upsets of the year at the Australian Open when she beat Williams in the quarterfinals.
"It will be epic," said Stephens, who downed American compatriot Jamie Hampton 6-1, 6-3. "I'm really looking forward to it. See what happens."
The chances of lightning striking twice for Stephens appears slim, as Williams, since a first-round exit at last year's French Open, has won 94 of 99 matches and earned 13 titles, including at three of the past five Grand Slam tournaments.
"''It's going to be tough. Sloane's playing so well," Williams said. "Regardless, there's definitely going to be an American in the quarterfinals."
Another Grand Slam winner, Li Na, also showed some championship form on Ashe. This time, her opponent, Laura Robson, looked very much like a teenager.
The fifth-seeded Li avenged her third-round upset loss to the young Brit at last year's U.S. Open, winning in straight sets at the same stage at Flushing Meadows.
Li came from a break down in the second set for a 6-2, 7-5 victory, crediting a pep talk from coach Carlos Rodriguez.
"After the talk I was feeling much, much better," she said. "Because before I never try to share the feeling with the team."
Third-seeded Agnieszka Radwanska, No. 9-seeded Angelique Kerber and No. 9 Jelena Jankovic all advanced in straight sets.
Wimbledon runner-up Sabine Lisicki, seeded 16th, won't be making a run at Flushing Meadows after she was eliminated in straight sets by Ekaterina Makarova. The 24th-seeded Russian won 6-4, 7-5.
Fifth-seeded Tomas Berdych beat Denis Kudla of the U.S. 7-6 (3), 7-6 (3), 6-3. American Tim Smyczek, ranked 109th, reached the third round at a Grand Slam tournament for the first time. He edged 73rd-ranked Alex Bogomolov Jr. in five sets, needing nearly four hours to win 3-6, 7-6 (6), 2-6, 6-4, 6-4.
