The reigning champion completely blew Adrian Mannarino away, claiming the first set 6-0 in a blistering 16 minutes, dropping just five points in the process.
Big-serving Anderson had never reached the final eight at the All England Club nor had he beaten Gael Monfils, but after a gruelling 7-6 (4), 7-6 (2), 5-7, 7-6 (4) triumph over the Frenchman in the fourth round, he can now tick both off his list.
However, should Federer make the final on Sunday, he might not enjoy the kind of undivided love and attention he normally would from the adoring Wimbledon fans.
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 previous year.
"It was great to win that first set so quickly", Federer told the BBC.
He has fully-justified his seeding of eight and was mentally rock-solid in winning three tiebreaks against Monfils in his four-set win on Court One.
He was down a break in the third set but broke right back for 3-3 and then converted his third match point when Vesely missed a backhand.
Mannarino was nevertheless able to frustrate his illustrious rival in the third set, even threatening to break for a 5-3 lead.
Monday's win took Nadal, 32, into a 35th Grand Slam quarter-final.
"I am not saying I am not excited to play against Roger in the final", he said. He rarely drops service and tends to win points on the first serve rather than wasting effort and going to a second.
Bertens, who ousted Pliskova and Venus Williams in the first round, reached the French Open semi-finals in 2016.
Below is a breakdown of each draw and a look at the four players with the best chances to advance to the men's and women's finals. "Luckily for me it didn't happen", Djokovic said after he romped to a 6-4 6-2 6-2 win to reach the last eight for a 10th time.
Nadal, a two-time Wimbledon champion, reached his first Wimbledon quarterfinals since 2011, when he was runner-up to Novak Djokovic in 2011.
"I'm more concerned the World Cup final will have issues because the Wimbledon final is going on", said the Swiss.
The Russian, 21, won her first title past year and reached the French Open quarter-finals last month.
Nadal, who plays at a slower, more deliberate pace, had no trouble with 93rd-ranked Jiri Vesely either, dismissing him, 6-3, 6-3, 6-4, in less than two hours.
In her third Wimbledon quarterfinal, Cibulkova faces former French Open champion Jelena Ostapenko.
On the bottom half of the bracket, it'll be 12-time major champion Djokovic against 2014 U.S. Open runner-up Kei Nishikori, and No. 2 seed Nadal against either 2009 U.S. Open champion Juan Martin del Potro or Gilles Simon.
All England Club chief executive Richard Lewis, meanwhile, says Wimbledon organisers will not alter the schedule to accommodate a potential England final appearance. That's always the idea for me in practice or matches, keep it entertaining, keep things going.