CINCINNATI — Roger Federer began his US Open preparation with a quick 6-4, 6-4 defeat of Peter Gojowczyk in his first ATP Cincinnati Masters appearance since 2015.

The 20-time Grand Slam champion, who turned 37 last week, is pacing his tennis year, playing a limited schedule and skipping events when he feels the need to rest.

He has missed the last two editions of this tournament because of injury.

Eighth seeded Petra Kvitova used her precision serve to overpower Serena Williams 6-3, 2-6, 6-3 in their second round match Tuesday night.

Federer’s defeat of the 47th-ranked German in 72 minutes marked his first step toward a possible eighth title at the tournament.

“I felt good in that first match, to be honest, walking out, hardly any nerves. I think I knew what I had to do,” Federer said.

“It’s fast-court tennis. I knew my opponent was going to go for it and take big cuts at the ball. So there is only so much you can really do.”

The contest was the first for the Swiss since losing to Kevin Anderson in five sets in the Wimbledon quarterfinals on July 11.

Eighth seed Dominic Thiem was forced to withdraw without hitting a ball. He was hit from a virus.

The Austrian played just one losing match last week in Toronto on the hardcourts since making a late switch from post-Wimbledon clay.

Nick Kyrgios served 39 aces, including one to save match point, to power into the second round with a dramatic 6-7 (2/7), 7-5, 7-6 (11/9) win over Denis Kudla.

Last year’s losing finalist finally saw off the American on his sixth match point.

The Australian will next face Croatian Borna Coric, who beat Daniil Medvedev 6-2, 6-3.

Weekend Toronto finalist Stefanos Tsitsipas tired late in a 7-5, 6-3 loss to Belgian 11th seed David Goffin.

South Korea’s Chung Hyeon rallied past a struggling Jack Sock for a 2-6, 6-1, 6-2 victory.

Unseeded Milos Raonic advanced past Serb Dusan Lajovic 6-3, 6-3 at the combined ATP and WTA event, the last major tune-up prior to the US Open on August 27.

In the women’s draw, the second set of the Kvitova-Williams contest was significant for Williams because it was her first set win this season against a top 10 opponent.

The 23-time Grand Slam champion won her first round match over Daria Gavrilova in straight sets, 6-1, 6-2, Monday, but appeared to run out of gas in the third set against Kvitova.

Just two weeks ago, Williams suffered the worst defeat of her career in San Jose when she was crushed 6-1, 6-0 in 51 minutes by world No. 39 Johanna Konta.

“I’m still at the very beginning. You know, this is a long comeback. I just began. Definitely at the very, very beginning,” Williams said. “I’m getting there, and I’m going to just continue to work hard, and hopefully I’ll start winning more matches.”

Czech ninth seed Karolina Pliskova made a personal breakthrough as she beat Agnieszka Radwanska for the first time after seven previous straight-sets losses to the Pole, winning 6-3, 6-3.

Australian 16th seed Ashleigh Barty defeated Czech teenager Marketa Vondrousova 6-3, 7-5, while 14th-ranked Elise Mertens topped Magdalena Rybarikova 6-4, 6-2. — AFP