Second seed Angelique Kerber stayed on track in her quest to unseat Serena Williams as world No.1 by beating Mirjana Lucic-Baroni of Croatia 6-2 7-6 (9-7) on Wednesday to reach the third round of the US Open.

Australian Open winner Kerber rifled home an ace to finish the first set against the free swinging, 34-year-old Lucic-Baroni, then won a see-saw second set in which each player was broken three times on the way to a tiebreaker.

The Croat held two set points during the decider, and three overall, before losing it 9-7.

The left-handed German was one win away in Cincinnati from ending Williams’ long reign as No.1 before losing to Czech Karolina Pliskova in the final and has another chance to leapfrog the American at Flushing Meadows.

Lucic-Baroni raised her game in the second set, but could not overcome the steady Kerber as the big-hitting Croat blasted 37 winners while throwing in 55 unforced errors.

“I played very well in the first set,” said Kerber, who also reached the Wimbledon final where she lost to Williams.

“I moved good, I played good. I played my game.

“In the second set, I was 4-1 up. It was still good for me, but I think she was playing better and she was going for it. Then she was not making too many mistakes like in the first set.”

Kerber had to battle to avoid the uncertainty and labours of a third set.

The German faced a set point in the 10th game before holding for 5-5.

Kerber fought off two more in the tiebreaker, with Lucic-Baroni serving with a 6-5 lead and again when the left-hander was serving down 6-7. Three errors by the Croat from that moment ended the match.

“When you win a set like this, you know that you can win when it’s really close,” Kerber said.

“This is what actually makes me like believing in my game again.

“I know if I’m down I can turn around the match. It’s good to have a set like that.”

Kerber next faces the winner of the American qualifier Catherine Bellis.