World number 115 Beatriz Haddad Maia of Brazil stunned Pliskova in straight sets to reach the round of 16 at a WTA Premier 1000 event for the first time.
The 15th and 16th seeds, Gauff and Andreescu, also exited in two sets, albeit to seeded players.
Haddad Maia lost in the final round of qualifying but made the main draw as a lucky loser when Nadia Podoroska withdrew through injury, and she has made the most of that reprieve with a 6-3 7-5 defeat of the world number three.
She had faced Pliskova once before and it did not go well, a 6-1 6-1 rout at the 2018 Australian Open, but the Czech struggled to find her trademark serve amid powerful winds in the California desert.
Pliskova suffered 12 double faults and won just 43.4 per cent of points on her serve, whole Haddad Maia saved nine of the 14 break points she faced on her own serve.
Haddad Maia next faces 18th seed Annett Kontaveit, who ousted Andreescu 7-6 (7-5) 6-3 to end the Canadian's dreams of a repeat.
Kontaveit has won 15 of her last 16 matches, winning titles in Cleveland and Ostrava during that stretch. Monday, she captured the first set on her fifth set point before rallying from a 3-1 deficit in the second to run the table and seal the win.
"It was extremely close throughout the match and I was just trying to stay tough. I was ready for a tough match," Kontaveit said. "She's such a good player, such a great competitor, so I knew it wasn't going to be over until it was really over."
Paula Badosa, the 21st seed, breezed past Gauff 6-2 6-2 as the American teen also had trouble with her serve, hitting just two aces after recording 12 in her previous match.
In a meeting of the last two defeated finalists in the tournament, 10th seed Angelique Kerber beat 20th seed Daria Kasatkina 6-2 1-6 6-4.
Third seed Barbora Krejcikova handled Amanda Anisimova with ease, 6-2 6-3.
Ons Jabeur, the 12th seed, had little trouble in downing 22nd seed Danielle Collins 6-1 6-3.