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The Serbian World number three has 22 Grand Slam titles.
The Wimbledon champion said she had been unwell for the last two days and was out of breath during the warm-up before her match against Sorribes Tormo.
The 29-year-old Pegula had no answer to Mertens' versatile game.
Elena Rybakina also booked a third round spot with a 6-3, 6-3 victory over rising Czech teenager Linda Noskova.
Sabalenka powered into the second round with a 6-3, 6-2 win over Ukraine's Marta Kostyuk, but was left perplexed by the taunts from a section the crowd.
The men's and women's champions will receive 2.3 million euros each.
The former US Open champion is recovering from surgery on her wrists and ankle.
The cancer was discovered in November last year. Navratilova was previously diagnosed with breast cancer in 2010 and recovered.
Sania, who is bidding adieu to the game after the ongoing Dubai Tennis Championships, says she never had the fear of losing in her heart because it makes a player defensive.
Djokovic's coach Goran Ivanisevic said after the final that the world No. 1 battled the injury, which would have forced most players to quit.
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