After a hard-fought victory over Romania's Elena-Gabriela Ruse in the first round, this was another gruelling encounter for Raducanu as she continues her return from injury.
The 21-year-old began well to go a double break up but was twice unable to convert when serving for the first set.
However, she showed her resilience in the breaker, setting up her first set point with a drop shot and - after a double fault - converting the second with a deft forehand.
Svitolina came fighting back at the start of the second with Raducanu saving two break points in the opening game, only for Ukraine's former world number three to convert the third.
Raducanu broke back immediately, but Svitolina made it three games against the serve in a row to restore her advantage.
Again, Raducanu hit back though with another break to make it 3-3 and from there it stayed on serve to set up another tie-break.
The Briton went up 3-1 before Svitolina reeled off six straight points to level the contest and never looked back.
Raducanu was showing signs of fatigue with two unforced errors gifting Svitolina a pair of break points in the first game of the third set. They were repelled, with a third saved with an ace, but a double fault eventually gave Svitolina the break.
There was no way back for Raducanu, who looked understandably weary after a long injury absence from the tour, and an energised Svitolina ruthlessly finished the job.
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