Second seed Federer reached his 10th US Open quarter-final in the last 11 years with a comfortable 6-4, 6-3, 6-2 win over Spain's Roberto Bautista Agut while Monfils, the 20th seed, reached his second New York last-eight stunning seventh-seeded Grigor Dimitrov 7-5, 7-6 (8/6), 7-5 yesterday.
Federer, the 17-time major winner, leads Monfils 7-2 in career meetings, including their most recent clash in Cincinnati last month.
"It was a tough three-setter in Cincinnati," said Federer after winning his 25th night-time match.
Federer was barely troubled by Bautista Agut, the 17th seed who was trying to make a Grand Slam quarter-final for the first time.
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He broke in the third and fifth games for a 4-1 lead and despite surrendering one of the breaks in the eighth game, two successive aces sealed the opening set and there was no looking back for the 33-year-old.
Crowd favourite Monfils overcame a dramatic loss of composure in the second set to reach his second US Open quarter-final, four years after his first.
"I love to play in New York. There is so much energy and it helps me deliver my game."
Wimbledon semi-finalist Dimitrov, 23, was hoping to reach his third quarter-final at the majors this year but despite occasional breath-taking shot-making, he was undone by 38 unforced errors.
Monfils, who hasn't dropped a set at the tournament, raced through the first set on the back of a break for a 6-5 lead.
Still seething, the Parisian surrendered a break point by not returning the ball in the eighth game.