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.
Federer's defeat of the 47th-ranked German in 72 minutes marked his first step towards 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.
"It's nice to have played a match so that my last match was not the Anderson match... you've kind of turned the page. It's a good thing.
"The goal is now to recover from this match, take the positives with me. Of course the big goal is the US Open."
The contest was the first for the Swiss since losing to Kevin Anderson in five sets in the Wimbledon quarter-finals on July 11th.