In a contrasting match on the court, the 28-year-old emerged triumphant with a scoreline of 6-1 1-6 6-1.
Svitolina dominated the first set but encountered difficulties with her eye in the second. However, she regained her composure and secured the victory.
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On court 12, Karolina Muchova, the runner-up in the French Open, suffered a surprising first-round defeat to Jule Niemeier.
The Czech 16th seed sustained a leg injury after stumbling in the deciding set and was defeated 6-4 5-7 6-1 by the German player, who reached the quarter-finals at Wimbledon last year but is ranked 87 places lower than Muchova.
Although Svitolina’s win against Mertens may be viewed as an unexpected outcome, the world number 76 has reached the semi-finals of two Grand Slams.
Her ranking declined only after taking a break from the sport to start a family last year.
She made her return to the tour in April following the birth of her daughter in October 2022, reaching the French Open quarter-finals last month and securing a comprehensive victory over seven-time Grand Slam champion Venus Williams in the first round of Wimbledon.
Svitolina will now face Sofia Kenin, the winner of the 2020 Australian Open, in the third round.
The American qualifier comfortably defeated China’s Wang Xinyu 6-4 6-3 on Thursday.
Two other Ukrainian players, Lesia Tsurenko and Anhelina Kalinina, also achieved victories.
Kalinina had to wait an additional two days to play her first-round match against Spain’s Jessica Bouzas Maneiro due to rain delays at the All England Club.
She emerged victorious with a score of 6-4 6-3. Tsurenko advanced to the third round for the third time with a straightforward 6-4 6-1 win over Czech player Katerina Siniakova.
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Furthermore, two-time major champion Victoria Azarenka progressed with a dominant 6-3 6-0 victory over Argentina’s Nadia Podoroska.
Former US Open winner Bianca Andreescu also won her delayed first-round match against Anna Bondar, prevailing with a scoreline of 6-3 3-6 6-2.
