Still seeking her first Grand Slam title since motherhood, she fought her way to a taxing 6-0, 4-6, 6-3 fourth-round win over Kanepi and into Tuesday's quarterfinals.
Williams said that everyone should "be completely grateful and honored" at how both men have done so much for the "greater good".
"It wasn't an easy match at all", said Williams, who last won the US Open title in 2014. Although she didn't know they were at the match as she played (ultimately defeating Venus), she candidly shared her support of the football players' protests during a post-match news conference.
Stephens could be headed for a semifinal meeting with Williams, although Williams acknowledged that in Pliskova she'll face a player with plenty of weapons in addition to her big serve.More news: Steven Gerrard goes after the referee following defeat to Celtic
"On clay, I think it's one of the biggest challenges in sports to beat this guy or to compete with this guy", Thiem said. "Winning a big game and a very important game and a really tight game, I think it was just a relief".
"Fortunately, I don't really feel pressure because I'm on this journey of getting back to where I was and I'm kind of enjoying that to be honest".
Serena Williams at the US Open on 28 August 2018. She was already a favorite, if not the favorite, to win the tournament after reaching the Wimbledon final in July, though she lost two of three matches during the hard-court swing before the U.S. Open.
Williams, chasing a record-equaling 24th grand slam, is playing her seventh tournament - and a third grand slam - since giving birth to daughter Olympia last September. "Nobody was expecting me to get that far", Pliskova said after beating No. 18 Ashleigh Barty 6-4, 6-4.More news: Alberta government to provide financial update on heels of Trans Mountain bombshell
However, Williams's relative lack of matches means that her concentration can waver, and whereas she made only two unforced errors in the opener she produced six in the first three games of the second.
"We've been waiting to see Serena at the level she was at before her pregnancy".
However, it was Williams' lightning fast start that sent fans into a spin on social media - the American seizing the first set from Kanepi in just 18 minutes. Nadal leads the series 7-3. "I hope to be ready to make that happen".
The American struck 17 winners and controlled play from the baseline, ran relentlessly to extend the points, dominated in the longer rallies and was also helped by her opponent's struggles on serve.More news: Trump says U.S. did ‘fantastic job in Puerto Rico’ after Maria