A day after saving two match points at the Madrid Open, Federer squandered two match points himself in the quarterfinals against Dominic Thiem on Friday, losing 3-6, 7-6 (11), 6-4.
Nadal cruised to a 6-3, 6-3 win over Canadian teenager Felix Auger-Aliassime to reach the third round in the Spanish capital.
Roger Federer skipped the entire clay season, including the French Open, in recent years to prepare well for the Wimbledon.
The 21-year-old Zverev won his eighth career title and second of the season after also winning the Munich Open last weekend.
Thiem beat the sixth-seeded Anderson after breaking both of his first service games in each set.
Nadal hadn't lost a single set on clay since falling to Thiem at the Rome Open quarterfinals one year ago.
Kiki Bertens beat seventh-seeded Caroline Garcia 6-2, 6-2 to advance to the Madrid Open final on Friday.
Pliskova's only prior victory from a previous seven matches against Halep was in the 2016 Fed Cup.
Djokovic lost in the third round in Monte Carlo and in the second round in both Miami and Indian Wells. The 12th-ranked Serb also failed to advance past the last 16 at the Australian Open.
Top-seeded Simona Halep reached the third round by beating Elise Mertens 6-0, 6-3.
Djokovic broke serve late in each set to get past the 20th-ranked Nishikori after nearly two hours in the Magic Box.
Nadal has said that despite a torrid start to his clay-court campaign it was unlikely he would be able to overcome an injury hiatus earlier in the season.
Williams, a 23-time Grand Slam champion, returned to the tour in Indian Wells this year after a 14-month absence because of the birth of her daughter.
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