Pliskova, the three-time WTA tour ace leader who briefly ascended to world number one previous year, has surprised Williams before at the US Open, beating her to reach her first Grand Slam final in 2016.
Pliskova offered this guess about what was happening to Williams: "Maybe she was a little bit nervous".
With her older sister, Venus - the woman she beat in the third round - in her guest box, Williams looked tight.
Oudin never made another Grand Slam quarterfinal, and she advanced past the first round at a major on just two more occasions (the French Open in 2012 and 2013).
Williams has performed wonders already by reaching the Wimbledon final, less than 11 months after the birth of her daughter Alexis Olympia.
She avenged a semi-final loss to Pliskova in the 2016 US Open and notched her first win over a top-10 player since she returned in March after the birth of daughter Olympia in September of previous year.
When someone urged her to raise her level in the second set, Stephens replied, "I'm trying!"
'I just want to be able to get past the semis here.
"When you don't play big points well, the match can get away from you", she said. "I'm going to enjoy it the best I can". "I know she can be off". Then I thought to just try making less errors, because at that point I was missing a lot of shots.
Slowly, point by point, Williams relaxed, started to better predict and return Pliskova's powerful serves and began controlling points and winning games.
Williams was on track to meet Stephens in the semi-finals but her third-seeded countrywoman was dumped out of the tournament via a 6-2, 6-3 loss to 19th seed Anastasija Sevastova. The first time, Williams had arrived in NY in search of the calendar grand slam - an extraordinary feat last achieved by Steffi Graf in 1988. She won the 2011 mixed doubles title at the US Open with Jack Sock, and her lone WTA singles title at the 2012 Aegon Classic.
She won the first four games - extending her streak to eight straight games - to take a 4-0 lead, completely shutting Pliskova down.
Soon after that, Williams went from trailing 4-2 to not only taking the first set but also leading 4-0 in the second.
Serena Williams of the United States hits to Karolina Pliskova of Czech Republic in a quarter-final match on day nine of the 2018 U.S. Open tennis tournament at USTA Billie Jean King National Tennis Center.
After the match, Stephens refused to blame the heat - or the sinus infection she said she has been playing with since Monday - and instead cited her failure to take advantage of early opportunities to get ahead on Sevastova's serve. But as Williams started to find her groove she held and then broke serve to tie it 4-4. "It's been a few, couple, rough semis for me", Williams said.