Poland's Radwanska, the number one seed in the absence of Serena Williams, lost 6-4, 6-7 (3/7), 6-3 to the rejuvenated Dominika Cibulkova of Slovakia.
Radwanska, a semi-finalist in 2012 and 2014 in the Spanish capital, already knew the dangers posed by Cibulkova after her opponent came within a point of victory in their last meeting at Indian Wells in March.
Cibulkova, a former world number 10 and Australian Open runner-up, was always going to be a dangerous floater having won her fifth career title last time out in Katowice three weeks ago.
However, Kerber was outplayed by world number 33 Strycova, who she had beaten 6-1, 6-1 in Miami back in March.
"I'd win four games in the matches we played before," said Strycova.
"I went into this match thinking I had nothing to lose. I mean, it can't be worse than Miami."
Losses for Radwanska and Kerber mean Garbine Muguruza is the highest seed left at the key clay-court event and the fourth-ranked Spaniard sealed her place in round two with a 6-2, 7-5 win over Anna Schmiedlova.
- Azarenka extends run -
========================
Former world number one Victoria Azarenka stretched her winning streak to 15 matches after winning in Indian Wells and Miami as she overcame some stiff first set resistence from Britain's Laura Robson to win 6-4, 6-2.
Azarenka could meet defending champion and fifth seed Petra Kvitova in the quarter-finals as the Czech had no trouble in disposing of Lara Arrubarrena 6-3, 6-2.
German Laura Siegemund continued her great start to the clay season after reaching the Stuttgart final as a qualifier as she dumped out ninth seed Svetlana Kuznetsova 6-0, 3-6, 6-3.
Eighth seed Carla Suarez Navarro came from a set down to beat Hungary's Timea Babos 3-6, 6-2, 6-3.
Ana Ivanovic also had to go the distance to see off Katerina Siniakova 6-3, 3-6, 6-4 while 2014 French Open runner-up Simona Halep, the sixth-seeded Romanian, swept past Japan's Misaki Doi 6-0, 6-3.
Also shrugging off jet-lag was Czech 11th seed Lucie Safarova, the champion in Prague on Saturday, who beat Coco Vandeweghe 7-6 (7/4), 6-1.
Australia's Samantha Stosur, beaten by Safarova in the Czech final 24 hours earlier, was also a winner, seeing off home player Sara Sorribes 6-1, 6-3.
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