Elena Svitolina, who came within two wins of becoming world No. 1 in January, maintained her ambitious momentum to reach the top by surviving a tricky start to her Wimbledon build-up on Tuesday.

The second-seeded Svitolina stumbled within sight of a two-set victory, and briefly faltered again in the last set before beating Donna Vekic of Croatia 6-1, 3-6, 6-1.

Svitolina showed glimpses of the tenacious movement and consistently ferocious drives which have earned her the best win-loss record on the WTA tour since the beginning of last year, but also revealed glimpses of insecurity on the lush, low-bouncing surface.

Despite carving a lead of a set and 3-1, her gradually increasing attempts to win points in the forecourt were of variable quality, while Vekic, a former runner-up here, began to contain and counterattack more effectively.

Svitolina nearly let slip another lead of 3-1, in the last set, needing to save two break points on her next service game - one with a fine serve, and the other with a net attack finished off at the third attempt.

Eventually, the Ukrainian's determination to adapt tactically to a surface on which she has yet to progress beyond any quarterfinal paid timely dividends, and she accelerated toward the finishing line at a canter.

"I was just trying to play well and to dominate, but she played a couple of great points to break back - which is always nice to have," said Svitolina, apparently meaning she was pleased to gain extra practice on such a technique-testing surface.

"It was difficult for me because she hit the ball very flat and the first match on grass is always a challenge."

She next faces Alize Cornet of France, who notably beat Serena Williams at 2014 Wimbledon, and who outlasted former top-10 player Ekaterina Makarova of Russia, by 5-7, 6-4, 6-1.