"It's important to get through the first week with a good feeling and I think I got that," said Federer. "The first match with the walkover saved me a lot of energy, crucial energy. We go one round at a time.
"The first goal is to get through to the second week and I am happy to sit back and relax and then come back on Monday."
Eighth seed Dominic Thiem progressed to the second week for the first time with a 7-5, 6-4, 6-2 result over American Jared Donaldson. The Austrian next faces former finalist Tomas Berdych. The Czech No. 11 seed easily defeated David Ferrer of Spain 6-3, 6-4, 6-3.
On the women's side, former finalists Garbine Muguruza and Angelique Kerber will face off for a place in the quarterfinals on Monday after contrasting but impressive third-round performances.
Muguruza, who was beaten by Serena Williams in the 2017 final, defeated Romania's Sorana Cirstea 6-2, 6-2 while world No. 1 Kerber fought back from one set down to beat American Shelby Rogers 4-6, 7-6 (2) 6-4.
Danish fifth seed Caroline Wozniacki, Polish ninth seed Agnieszka Radwanska and Russia's seventh seed Svetlana Kuznetsova all advanced to the last 16.
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