Venus Williams is also into the fourth round of another major after beating Maria Sakkari of Greece 6-3, 6-4.It was Williams' 74th win at the US Open, breaking a tie with Steffi Graf for fourth most by a woman in the Open era.
While Sharapova didn't play her best match as she hit several unforced errors, the young American really proved to be a tough test for the former world number one.
Sharapova twice broke the Babos serve when the Hungarian was serving for the opening set but then lost the tiebreak 7-4.
It was only in the decider that the five-time Grand Slam showed her class to clinch a 6-7 6-4 6-1 victory.
"She's feisty. I know I have to come out, play well, have you all [the crowd] behind me and get a win."
Only current number one Karolina Pliskova and fourth-seeded Elina Svitolina can deny Muguruza reaching the top spot for the first time.
Sharapova, who returned from her ban in April, was snubbed for a wildcard in the French Open and injured for Wimbledon but was given a US Open wildcard despite playing only one hardcourt tuneup match due to a forearm injury.
"When you see the stress on the scheduling system because of the sheer number of matches that had to be played, it would be tough for it to be flawless for everyone", said Widmaier. The No. 18 seed advanced to the second week after Britain's Kyle Edmund retired Friday with a neck injury. No qualifier had reached the last 16 since Gilles Muller in 2008.
"I struggle playing at night at this tournament", Isner said.
Schwartzman, ranked No. 33 in the world, will next face 16th seed Lucas Pouille, a 2-6, 6-3, 6-4, 6-4 victor over Russia's Mikhail Kukushkin.
"Every day that I have another chance to play out here at the US Open is a special day".
Sam Querrey will look to end a grand slam drought that dates back to 2003 on the American men's side when he battles Radu Albot of Moldova.
Bopanna and Uruguay's Pablo Cuevaslost to Fabio Fognini and Simone Bolelli, 5-7, 6-4, 6-4 in an hour and 47 minutes in the men's doubles second round match.
The 10th seeded American, who was knocked out 6-4, 6-3, 7-6 (7-5) by German Mischa Zverev, also added he was baffled at his poor form at night in his home grand slam.