With all of the top-10 seeds out of the tournament, Williams is the comfortable favourite heading into the last-eight - a status she's more than used to after a remarkable career spanning more than two decades.
The Dutchwoman's 6-3 7-6 (1) win means that for the first time since seedings were introduced at Wimbledon in 1927 none of the top eight in the women's draw made the quarter-finals.
Williams reached her 13th Wimbledon quarterfinal by beating Russian qualifier Evgeniya Rodina 6-4, 6-2 on Monday, and never looked likely to join the parade of favorites who have been eliminated.
The exit of former world number one Pliskova came after the women´s draw was blown wide open by surprise defeats earlier in the tournament for Maria Sharapova, Petra Kvitova, Caroline Wozniacki, Simona Halep and Sloane Stephens.
Williams continues her quest for an eighth title later against Russian qualifier Evgeniya Rodina, with the victor to meet Italian Camila Giorgi, who advanced to her maiden grand slam quarter-final with a 6-3 6-4 defeat of Ekaterina Makarova.
Also, the last of the women's top-10 seeds was knocked out at Wimbledon.
"It was tougher than the scoreline, " Williams said.
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.
"I think", Federer said when it was over, "I can be very pleased". She is seeded 25th after missing last year's tournament while pregnant.
"I'm a perfectionist, I always find something", the 36-year-old responded when asked about her near-flawless display.
Dominika Cibulkova faces Jelena Ostapenko, Daria Kasatkina battles Angelique Kerber, and Kiki Bertens plays Julia Goerges in the other quarterfinal clashes. So hopefully I'll start feeling better mentally as well as I am on the court'.
Both Anderson of South Africa and the 44th-ranked Monfils of France were bidding to reach the quarterfinals for the first time on their 10th appearance at the All England Club.
"It sounds pretty odd when you saw my record from the last five years here".