(Reuters) - Angelique Kerber took a confident first step on a path that could lead her to the top of the world rankings with a straight sets victory over Kristina Mladenovic at the Western & Southern Open in Cincinnati on Wednesday.

The German world number two, fresh off claiming a silver in the women's singles at the Rio Olympics, stormed through the opening set then fought off her gritty French opponent to post a 6-0 7-5 second-round triumph.

A victory in the hardcourt warm-up event for the U.S. Open, the year's final grand slam, would lift Australian Open champion Kerber past the absent Serena Williams as world number one.

Joining Kerber, who was beaten by Williams in last month's Wimbledon final, in the third round was the in-form third seed Simona Halep.

The Romanian ran her winning streak to 11 as she brushed aside German qualifier Annika Beck 6-3 6-1, showing off her improved serve with seven aces after a downpour delayed the start of play for a couple of hours at the rain-plagued event.

"I'm really happy I'm back here in Cincinnati, I have great memories from last year. I played very good tennis today and I'm really happy with my game," said Halep, the runner-up last year, who is coming off titles in Bucharest and Montreal.

French Open champion Garbine Muguruza started slowly against American Coco Vandeweghe before the Spaniard rolled to an easy victory after a tight opening set in a 7-6(4) 6-2 second-round triumph that marked her first win in Cincinnati.

"I'm so happy I finally won my first match," said Muguruzu, who has been the victim of tough draws on her previous visits.

The Spaniard was so eager to get off on the right foot this year that during Tuesday's day of rain, she was seen grabbing a squeegee mop to dry a practice court so she could hit balls.

"I think there is a black cloud following the WTA this year," she said about persistent rain. "I wanted to practice and I couldn't, so I took it into my own hands to do it."

(Reporting by Larry Fine in New York; Editing by John O'Brien)