Hingis is currently ranked 13th in the world

Hingis, who has been struggling with a hip injury, won 7-5 6-2 against Wimbledon quarter-finalist Krajicek.

"This is the first time I feel like myself since March," said Hingis. "I feel fresh and motivated again."

Second seed Jelena Jankovic and Wimbledon finalist Marion Bartoli were among the other winners on Tuesday.

Jankovic marked her return from a four-week layoff with a 6-3 6-0 thrashing of American Vania King.

"It was my first match since I came back from vacation and I'm still jet lagged so it was tough, but it was a good effort overall," said the Serbian.

"I focused on trying to get used to the atmosphere and the ball. I had a cup of coffee before coming on court and ended up moving well. I hope I'll get better and better."

France's Bartoli beat Aiko Nakamura 7-6 6-1 and appeared to have recovered from the stomach illness and leg injury that hampered her at Stanford last week.

"Any time you play someone who reaches a Grand Slam final, they have a target on their back," said Bartoli.

"Now some players feel like they have nothing to lose against me but I like the challenge."