But fellow injury patient Stan Wawrinka opened with a defeat of 12th seed Diego Schwartzman 6-2, 4-6, 6-3.
Federer has enjoyed an incredible renaissance since undergoing knee surgery in February 2016, winning two Australian Open titles and an eighth Wimbledon crown.
But the 23-times grand slam champion dug deep in the second, thumping serves and blasting returns to the delight of the supportive crowd under the lights.
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 of Britain. Cincinnati was Williams's sixth tournament since giving birth last September. She has dealt with blood clots and recently said she has been struggling with postpartum emotions. "'There's a lot of things that I can say I like about Rafa", said Dimitrov.
"I started, in the beginning, with many more five-setters in finals and then they completely went away".
"I competed too hard in the first set to sort of just let the match slip and not compete, give myself a chance to win, at least".
The Cincinnati Masters is Federer's most successful Masters 1000 event, having won it seven times. I enjoy playing here because of my success, even more so, but I have always enjoyed coming here to Cincinnati, and now we do it as a family.
Tribute to Atal Bihari Vajpayee: Odisha Govt declares holiday tomorrow
Vajpayee's body will be taken to his New Delhi home and then to the BJP's office on Friday for people to pay their last respects. He was the prime minister who ordered nuclear tests in 1998, stoking fears of atomic war between India and Pakistan.
China to send negotiator to USA for trade talks this month
The offshore Chinese yuan rose briefly on the news against the dollar, strengthening to a high of 6.9165 before paring gains. The SCI 300 Index was up 0.59 per cent by mid-morning, having fallen as much as 1.8 per cent shortly after open.
Samsung launches pre-orders for Galaxy Note 9 in India
The device has an impressive 1 Terabyte of memory, which is expandable, so customers have the power to store more and delete less. They pointed out the South Korean tech giant's poor sales with the Galaxy S9 and S9+ series in the first half of the year.
"It's nice to have played so that my last match was not the Anderson match", Federer said.
"I've been practicing on hard courts, so it's not like I haven't played on hard courts for forever", said Federer who hasn't played on hard since Miami. Then, obviously, I hurt my elbow.
Canadian Denis Shapovalov beat USA tournament debutant Frances Tiafoe 7-6 (8/6), 3-6, 7-5 Sam Querrey beat ninth-seeded American compatriot John Isner 6-4, 6-7 (5/7), 7-6 (7/5).
South Korean Chung Hyeon rallied to beat Jack Sock 2-6 6-1 6-2 and set up a second-round clash with fourth seed Juan Martin del Potro. Sock has lost eight consecutive matches since May.
Elsewhere, there were first-round wins for Italian Camila Giorgi and Dutchwoman Kiki Bertens, who defeated American Coco Vandeweghe 6-2 6-0. Ashleigh Barty stopped wild card Marketa Vondrousova 6-3, 7-5. Ekaterina Makarova cruised past qualifier Ana Bogdan 6-3, 6-2.
Maria Sakkari, of Greece, returns to Naomi Osaka, of Japan, at the Western & Southern Open, Tuesday, Aug. 14, 2018, in Mason, Ohio.