Svitolina, ranked five, lost to an injured Victoria Azarenka in Doha last week and failed to take advantage of winning the first set as she fell 2-6 6-4 6-1 to 35-year-old Kuznetsova.
“I’m really disappointed with Doha and Dubai,” said Svitolina. “For sure it hurts but I have to analyse, I have to work on my fitness, I have to work on my game on the practice courts. There are still many tournaments this year and I have to move forward.”
Second seed Karolina Pliskova has also struggled so far in 2021 but she remains in the tournament after a 6-3 6-7 (5) 6-2 victory over Anastasija Sevastova.
Third seed Aryna Sabalenka defeated Alize Cornet 6-2 6-4 but fifth seed Kiki Bertens, who is on the comeback trail following Achilles surgery, lost 6-1 6-4 to Tereza Martincova.
French Open champion Iga Swiatek continued her winning run following her title in Adelaide with a 6-2 6-4 victory over Misaki Doi, and there were also wins for Belinda Bencic and Elise Mertens, but seeds Madison Keys and Marketa Vondrousova were beaten.
The latter fell 3-6 6-0 6-4 to Coco Gauff in a feisty match. Tension stemmed from Gauff querying with the umpire whether Vondrousova was allowed to catch a ball toss with her racket and subsequently saw the American teenager appear to aim a drive volley at her opponent.
Gauff, who turns 17 on Saturday, said: “It wasn’t meant to make her upset, it was just meant to ask the question to the ref if that’s allowed and he said yes. I could tell she was a bit frustrated by that. My personality, I fight fire with fire.”
Doha champion Petra Kvitova’s stay at the tournament was short-lived as she pulled out with a thigh injury trailing 6-2 3-4 to Jil Teichmann but Garbine Muguruza, who Kvitova beat in the final on Saturday, defeated Amanda Anisimova 6-4 6-2.
At the Abierto Zapopan in Guadalajara, Mexico, the Czech Republic’s second seed Marie Bouzkova, fourth-seeded Spaniard Sara Sorribes Tormo and eighth seed Kaja Juvan, of Slovenia, all reached the second round.
There were also first-round wins for home favourite Renata Zarazua, Slovakia’s Anna Karolina Schmiedlova and Switzerland’s Leonie Kung.
But Russian third seed Anna Blinkova was beaten 6-3 7-5 by Slovenia’s world number 93 Tamara Zidansek.
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