Former five-time champion Federer raced to 6-3, 6-0, 6-2 win over the left-handed world number 63, who has never beaten a top-10 player in seven attempts.
That grim statistic never looked like changing on Saturday as he was broken six times and managed just eight winners to Federer's 34.
Federer, seeded at seven in New York this year in what his lowest ranking for 11 years, next tackles fellow veteran Tommy Robredo of Spain, against whom he enjoys a 10-0 winning record.
Nadal, the 2010 champion, earlier cruised past Croatia's Ivan Dodig, 6-4, 6-3, 6-3, to set-up a last-16 clash with Germany's Philipp Kohlschreiber.
Victory in their fourth round ties on Monday will set-up a mouth-watering quarter-final between the two giants of the game.
"I was really pleased with the outcome. Adrian is capable of playing a great match," said the 32-year-old Federer.
"But there was a lot of wind tonight and maybe I had more variety than him and once I had the lead, it made it all easier."
Federer said he was ready for another tough encounter with 31-year-old Robredo despite his perfect record in meetings with the Spaniard, who has now made the fourth round for the eighth time.
"We both have a one-handed backhand, but maybe I have more power and variety in my game," said the Swiss.
"He plays well here. I thought he may have had an injury from the previous match but they can heal quickly."
Federer took his record in the night sessions at the US Open to 22-1 with a third career win in three meetings with 25-year-old Mannarino.
One break in the fourth game of the opening set was enough for the 17-time Grand Slam title winner, who then clinched three more breaks in the second as Mannarino's weak challenge fizzled out.
It got worse for the Frenchman, who had managed to make the fourth round at Wimbledon last month, as he was broken again in the third and fifth games in the decider, with Federer taking victory after a disappointing 82 minutes.