"In the second set, I was starting to [feel] the ball better and better. I think the key was, at the end, that I was fighting and I was never giving up at the end, doesn't matter how the score was."
Besides reaching the Wimbledon final last year, Kerber won the Australian Open and US Open. That made her only the fourth player in the Open era to reach three Grand Slam finals in the same season.
This year, Kerber lost in the fourth round at the Australian Open and then became the first top-seeded woman at the French Open to lose in the first round in the Open era.
After dropping the opening set against Rogers today, Kerber trailed 3-1 in the second, before turning things around. The top-ranked German will next face 2015 Wimbledon finalist Garbine Muguruza on Monday night (NZT).
Muguruza, the 2016 French Open champion, beat Sorana Cirstea 6-2, 6-2.
Raonic finished with more than twice as many winners (55) as unforced errors (26). He will be playing in the fourth round for the third time in four years.
"I did a lot of things well today," Raonic said. "I was efficient on my serve, created a bunch of opportunities - I started getting better and better there.
"Maybe at the beginning, I wasn't controlling the situation enough, but as the match went on, I felt like I was dictating more so from the baseline."
The Canadian will next face Alexander Zverev, who beat Austrian qualifier Sebastian Ofner 6-4, 6-4, 6-2.
Novak Djokovic, a three-time champion, also won. He was down a break early in the first set, but managed to beat Ernests Gulbis 6-4, 6-1, 7-6 (2).
Djokovic will next face Adrian Mannarino, a Frenchman who defeated Gael Monfils 7-6 (3), 4-6, 5-7, 6-3, 6-2.
Roger Federer and Dominic Thiem were also on the schedule for Day six at Wimbledon, ahead of the tournament's traditional break on the middle Sunday.
Other women's winners on Saturday included third-seeded Agnieszka Radwanska, Caroline Wozniacki, CoCo Vandeweghe, Svetlana Kuznetsova, Magdalena Rybarikova and Petra Martic.
For the men, Grigor Dimitrov, Sam Querrey and Tomas Berdych also advanced.