Five-time Wimbledon champion Venus Williams had to change her bra in a rain delay in 2017 as the pink straps were visible from her shoulders.
Frenchman Mannarino improved in the second and third set but was unable to trouble Federer as the 36-year-old clinched an impressive 6-0 7-5 6-4 triumph.
The result extended Federer's run of consecutive sets won at Wimbledon to 32, two short of his career best from 2005-06, while he has not dropped serve since the semi-finals past year.
Vesely, the world No 93, had never got beyond the fourth round of a Grand Slam, and never looked like causing the Spaniard too many problems.
Roger Federer is in the fourth round of Wimbledon. Of the five points he lost, three were in the final game, when he faced his first break point of the tournament - and answered it with an ace.
The blow appeared to suck the life out of Mannarino and he was broken in the next game before Federer served out for the match.
Nadal, whose 17 Grand Slam titles are eclipsed by Federer's 20 and the 23 owned by Williams, did not disappoint in the late afternoon sunshine as he dissected fellow left-hander Vesely with a typically rumbustious display.
The only significant test Williams should face in the bottom part of the bracket would come in the semifinals against Karolina Pliskova, Kiki Bertens or Julia Gorges.
Williams is 6-2 in her career against Kerber, but the match might be better than expected given the tight major finals played between the two in 2016. Federer has been the dominant player on grass on the men's circuit for more than a decade, but Nadal has experience of beating the Swiss legend on Centre Court at Wimbledon. He could not quite make it to a tie-break, though, with Federer breaking for 6-5 and then serving out the set. "I can only really practice it with my coach".
Strokes of Genius is a world-class documentary capturing the historic 13-year rivalry between tennis icons Roger Federer and Rafael Nadal.
"Novak (Djokovic) and Rafa (Nadal), all these guys are still in the draw", he said.