Federer cruises to Verdasco win
The 31-year-old Swiss took just over two hours to dispose of the Spaniard 6-3 6-3 6-4.
Federer, who won at Wimbledon earlier this year before claiming Olympic silver, hit 30 winners and faced only one break point in beating Verdasco, BBC reported.
"I was never really in big trouble on my service games," said Federer.
The winner of the match between American Mardy Fish and Frenchman Gilles Simon awaits Federer in the next round.
Federer was beaten in the semi-finals at the US Open last year when he let a two-set lead slip as well as missing out on two match points against eventual winner Novak Djokovic.
"I was thinking about that match today," said Federer, who returned to the number one spot after his Wimbledon triumph.
"I always believed I would get back to number one in the world and now that I am, it's amazing. It has been a great year."
Milos Raonic became the first Canadian to reach the fourth round since 1988 with an impressive 6-3 6-0 7-6 (7-3) victory over former world number four James Blake.
The 15th seed produced a masterclass in serving, hitting 28 aces and winning 89% of points on his first serve to set up a meeting with third seed Andy Murray.
Nicolas Almagro, Marin Cilic and Martin Klizan joined Federer in the next round thanks with respective victories against Jack Sock, Kei Nishikori and Jeremy Chardy.
There was British success in the men's doubles as Colin Fleming andRoss Hutchins beat Brian Baker and Rajeev Ram 7-5 6-3 to reach the third round, while Jamie Delgado and Ken Skupski progressed with a 7-6 (7-3) 7-6 (9-7) win over Jurgen Melzer and Philipp Petzschner.