"It was great to win that first set so quickly", Federer told the BBC. He did not disappoint - dissecting fellow left-hander Vesely with a typically rumbustious display.
After seven years of struggles, Rafael Nadal is finally looking like a contender again at Wimbledon.
So far this year, though, it has been like watching him on a Parisian claycourt rather than a London lawn, such has been the ferocity in his brutal groundstrokes and his boundless energy.
Camila Giorgi, who has beaten eight top 10 players during her career, is into her first Slam quarter-final, while Dominika Cibulkova reached the Australian Open final in 2014. Nadal has suffered some bad losses since reaching the 2011 showpiece, falling to four players with three-digit rankings. But burly Czech Vesely, more unsafe than his 93rd ranking suggest, never got close to causing an upset. "I was inspired. I wanted to play exactly like him and do the same results".
When asked if he thought people watching the World Cup final on their devices simultaneously would detract from the atmosphere, Federer added: "It's going to happen anyway, if I'm going in the final or not, the Wimbledon final will take place, and so will the World Cup final". We can find reasons, knees, everything. In 2012, 2013, I was not able to compete.
Tomorrow, Federer will have the chance to break his own Wimbledon record of 34, recorded between...
The only hiccup was when the Czech managed to go a break up in the third, but his lead was just as quickly wiped out as the world no. 1 broke back immediately on his way to taking the match inside two hours.
Stefanos Tsitsipas can make history by becoming the first Greek player - man or woman - to reach a Grand Slam quarter-final if he beats USA ninth seed John Isner. Del Potro was leading 7-6 (7/1), 7-6 (7/5), 5-7 when his tie with Simon was halted for the night due to darkness.
They clapped and yelled when Federer's drop volley capped a 16-minute tour de force of a first set in which he won 21 of the first 23 points.
He will play South African eighth seed Kevin Anderson on Wednesday as he bids for a ninth Wimbledon singles title to draw level with record holder Martina Navratilova.
The second seed defeated Jiri Vesely 6-3, 6-3, 6-4 on Centre Court.
"Raonic is a danger man in that section with that serve - good luck to anybody with that - and he beat Federer last time when he got to the final".
At times it appeared the number two seed was playing on his beloved clay, such was the spin and bounce he extracted from the turf, but there was a brief hiccup in the third set.
The first set horror-show and an apparent groin injury did not stop the world number 26 from becoming the first man to earn break points against Federer at the All England Club this year.