Second seed Federer showed no mercy against Canadian Peter Polansky in a 6-2, 6-0 second-round thrashing which took just 52 minutes.
Federer converted on six of seven break points as he played for the first time since his Wimbledon final against Novak Djokovic.
"I was happy, I started well, and that's always helpful to play more freely," said the winner of his 41st match this season.
"I could have served better at times, but I felt I was moving wel," Federer said.
"For the start of a tournament it's never clear if that's going to be the case," he said.
"I'm very relieved and just really pleased."
It was much more difficult for Australian Open winner Wawrinka, who battled to a 4-6, 6-3, 7-6 (7/2) victory over Frenchman Benoit Paire.
The Swiss saved a match point in the tenth game of the final set and finally advanced with a running volley winner on the first of four match points.
Wawrinka took time away from the game after Wimbledon, skipping the ATP Tour's Gstaad tournament at home due to fatigue.
Federer is playing Canada for the first time since 2011 after winning titles in 2004 and 2006. He is in the hunt for an 80th career trophy.
Promising Australian teenager Nick Kyrgios defeated Santiago Giraldo 7-6 (7/3), 7-5 to set up a second-round meeting with Andy Murray.