Nadal, the 2010 and 2013 champion, took his perfect first round record in New York to 12-0 with a 6-1, 6-4, 6-2 win over Denis Istomin of Uzbekistan.
The Spaniard's reward for a fifth win in five meetings against the Russian-born player is a match-up with Italian veteran Andreas Seppi.
A wrist injury forced Nadal into an early retirement at the French Open and sidelined him from Wimbledon before a gold medal run in the doubles at the Olympics helped ease his misery.
Kerber needed just over 30 minutes to get her pursuit of a first US Open title off to a winning start.
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The second seed and Australian Open champion was leading Polona Hercog 6-0, 1-0 when the Slovenian called it quits, clearly wilting in the 33-degree heat, having won just nine points.
"It's not the way I wanted to win, but I am playing well and feeling good," said the German star.
Spanish third seed Muguruza carved out a gritty 2-6, 6-0, 6-3 win over Belgian qualifier Elise Mertens, ranked at 137.
But the French Open champion needed courtside treatment from a doctor after dropping the first set on the Louis Armstrong Court.
- Doctor's orders -
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The consultation certainly worked as she reeled off the next seven games to lay the foundation for her win.
Muguruza plays Anastasija Sevastova of Latvia for a place in the last 32.
French 13th seed Richard Gasquet, a semi-finalist three years ago, was the day's biggest casualty.
the exit before coming back from two sets down to beat 18-year-old compatriot Frances Tiafoe.
Isner, who fired 35 aces, triumphed 3-6, 4-6, 7-6 (7/5), 6-3, 7-6 (7/3) after three and a half hours against the youngest player in the draw.
Croatian seventh seed Marin Cilic, the 2014 champion, eased past Brazil's Rogerio Dutra Silva 6-4, 7-5, 6-1.
Flamboyant French 10th seed Gael Monfils took his summer hardcourt record to 15-2 with a 6-4, 6-2, 7-6 win over Gilles Muller of Luxemburg.
Monfils almost suffered a freak accident when a giant courtside clock fell towards him as he collided with the back wall, chasing down a Muller shot.
Svetlana Kuznetsova, the 2004 champion, needed only 58 minutes to beat old rival Francesca Schiavone 6-1, 6-2.
The pair famously played the longest women's match of all time at the 2011 Australian Open where Schiavone saved six match points in a four hour 44-minute marathon.
Double Wimbledon champion Petra Kvitova beat Jelena Ostapenko 7-5, 6-3 while former world number one and two-time US Open runner-up Caroline Wozniacki downed US qualifier Taylor Townsend 4-6, 6-3, 6-4.
The Flushing Meadows complex was showcasing its gleaming $600 million refit which includes a retractable roof over Arthur Ashe and a brand new Grandstand court.
Later Monday, world number one and defending champion Novak Djokovic, whose last major ended in a shock third round exit at Wimbledon, starts against Jerzy Janowicz of Poland.
Djokovic, the 2011 and 2015 champion, admits he is "not 100 percent" after suffering a wrist injury on the eve of the Olympics where he was a first-round loser.
Women's top seed Serena Williams and 2012 champion Andy Murray will get underway on Tuesday.
Williams is chasing a record seventh US Open and will equal Steffi Graf's record of 186 successive weeks at world number one.