“It’s nice of course to come back but you have a lot of pressure,” said Vinci who was ranked 43 in the world this time last year.
“Now I’m seven in the world — a lot of points to defend. But probably the key is don’t think about this.”
Kvitova, the 14th seeded Czech who recorded her best performance in New York 12 months ago when she made the last-eight, beat Turkey’s Cagla Buyukakcay 7-6 (7/2), 6-3.
Kvitova was in her trademark all-or-nothing mood, mixing up 31 winners with 30 unforced errors against her 26-year-old opponent, the first Turkish woman to play in the main draw at the tournament.
“If I make the second week, I’ll be happy,” said Kvitova, keen to dampen down expectations.
Up next for Kvitova is Ukrainian 22nd seed Elina Svitolina who put out Lauren Davis of the United States 6-1, 4-6, 6-3. Early winners in the men’s event were South Africa’s Kevin Anderson who saw off Canada’s Vasek Pospisil 7-6 (7/3), 6-4, 6-4.
Anderson reached the quarter-finals last year, beating 2012 champion Andy Murray on the way, but has been plagued by knee, shoulder and ankle injuries in 2016 which forced him to skip eight events.
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 US wildcard Ernesto Escobedo.
Later, Spanish fourth seed Rafael Nadal, the 2010 and 2013 champion, takes a 7-1 career record over Italy’s Andreas Seppi into their night time clash. Seppi, ranked at 87, has never got beyond the third round in New York but he is a former top 20 player who knocked Roger Federer out of the Australian Open two years ago.
Like Djokovic, Nadal is suffering the after-effects of injury after a serious problem with his left wrist sidelined him from midway through the French Open until the Rio Olympics.
Reigning Roland Garros champion and third seed Garbine Muguruza of Spain tackles Latvia’s Anastasija Sevastova.
Muguruza needed three sets to see off Belgian qualifier Elise Mertens in a first round tie which also saw her need a medical timeout after suffering heat exhaustion.
Angelique Kerber, the second seeded Australian Open champion who could depose Serena Williams as world number one, faces 34-year-old Mirjana Lucic-Baroni.
The veteran Croatian made the last 16 in 2014 having played her first US Open back in 1997.
