Milos Raonic was stunned by Lukas Lacko in the first round of the tournament.
The US Open, final Grand Slam of the season, starts on Monday at Flushing Meadows in New York.
Canadian sixth seed Raonic had knocked out Federer in the semi-finals in 2016, a defeat which led the Swiss superstar to shut down the rest of his season to rest a knee injury.
Roger Federer hit his 10,000th career ace in the eighth game of the first set.
Rafael Nadal needed all his trademark grit against Alexander Zverev, 19, dubbed "the future of tennis", and his superior fitness told as he ground out a thrilling 4-6, 6-3, 6-7 (5/7), 6-3, 6-2 win
Serena Williams thumped dangerous Swiss teen Belinda Bencic 6-4, 6-3 to enter the second round of the Australian Open.
Andy Murray, who saved a match point, lost the first set to Milos Raonic but won the next two sets on tie-break to reach the final of the ATP World Tour Finals on Saturday
Andy Murray brushed aside Stan Wawrinka in 86 minutes at London's O2 Arena to ensure he finished top of his group in the ATP World Tour Finals and avoided a last four clash with Novak Djokovic
Rafael Nadal's 2016 season was plagued by physical problems and he cut his campaign short in October to recover fully to target a return to Grand Slam glory in 2017
Andy Murray will move to the top of men's tennis rankings for the first time in his career after replacing long-time incumbent Novak Djokovic
John McEnroe made his announcement just two days out from the start of the 2016 US Open, the season's final Grand Slam event where world number six Milos Raonic is ranked as a potential title winner
Since losing the French Open final to Novak Djokovic in June, Andy Murray has won Queen's Club, a second Wimbledon title and successfully defended his Olympic crown in Rio
Serious questions have been asked about Tennis' future in the Olympics after 20 high-profile players withdrew citing a combination of security, injury and Zika virus concerns.
Milos Raonic, the world number seven from Canada who lost to Andy Murray in the Wimbledon final, said he had taken the decision "with a heavy heart".
Andy Murray joined the likes of Roger Federer and Novak Djokovic by becoming the latest father to win a Grand Slam title
Milos Raonic lost to Andy Murray in the Wimbledon final thwarting his bid to become Canada's first Grand Slam champion
Andy Murray defeated Milos Raonic 6-4, 7-6 (7/3), 7-6 (7/2) to win his third Grand Slam crown and become the first British man to lift multiple Wimbledon titles since Fred Perry in the 1930s