Novak Djokovic has been handed invaluable time to regain fitness after his US Open second-round opponent Jiri Vesely withdrew injured.
Marin Cilic, the 2014 US Open champ, also advanced to the third round.
World No 23 Ivo Karlovic is 2-1 head-to-head against Djokovic.
"I knew today I needed to be focused because I've played her".
Angelique Kerber, the second seeded Australian Open champion who could depose Serena Williams as world number one, faces 34-year-old Mirjana Lucic-Baroni.
Wimbledon runner-up Milos Raonic had 15 double-faults and lost to 120th-ranked qualifier Ryan Harrison of the United States 6-7 (4), 7-5, 7-5, 6-1 in the U.S. Open's second round.
It certainly seemed to work - she reached the quarterfinals here for the first time.
Britain's Kyle Edmund backed up his first round win over world number 15 Richard Gasquet with a 7-5, 6-4, 6-4 victory over USA wildcard Ernesto Escobedo on the back of 53 winners.
I think Djokovic could drop a set again, but still has enough to find a way to win against Vesely.
Asked about playing an opponent who defeated him in their only meeting, he ticked off all the reasons that might not be relevant: "Different surface, different circumstances, best-of-five".
The first scare for the American occurred in the second game of the second set when he had to save 2 break points but the rest of the set was fine for him, scoring another break in game 5 to take it 6-4.
The 106th-ranked Darcis also faced the extra fatigue of going through qualifying to make the main draw.
Isner improved to 9-0 in U.S. Open second-round matches. He had 38 aces Wednesday, when he received treatment on his right knee and for blisters on his foot. The most recent match was in the 2013 US Open, a match Djokovic won in four sets.
Slovak 12th seed Dominika Cibulkova overcame a left-thigh injury to see off Russia's Evgeniya Rodina 6-7, 6-2, 6-2, winning 17 of the last 18 points.
Vesely first suffered the injury last week, forcing him to pull out midway through a tournament in Winston-Salem, and it was further exacerbated by his five-set match of nearly four hours in the first round on Monday.
Vesely's issue is a left forearm problem which also saw him pull out of the ATP Winston-Salem tournament earlier this year.
Two-time Wimbledon victor Petra Kvitova, the 14th seeded Czech who recorded her best performance in NY 12 months ago when she made the last-eight, beat Turkey's Cagla Buyukakcay 7-6 (7/2), 6-3.
After a blistering start to the year when he won the majors in Australia and France, he has been struggling for form and was ousted in the third round at Wimbledon before crashing to a shock first-round exit at the Olympic Games. Vinci needed just 22 minutes to win the first set. Then he beat Roger Federer in the semifinals at the All England Club in July to reach his first Grand Slam final, before losing to Andy Murray.