Kerber enjoyed a superb 2016, winning both the Australian and US Opens as well as rising to the top of the WTA rankings. But she has struggled for form this year, and crashed out in the opening round at Roland Garros.
The German has looked to be playing her way into some form at The Championships, but made a slow start against Rogers. She lost her second service game and was unable to find a way back into the first set, losing 6-4.
Rogers broke again at the start of the second set and raced into a 3-1 lead. But Kerber immediately hit back, before holding her nerve in the ensuing tiebreak. Buoyed, she went on to win the third set and the match, preserving her No 1 ranking for another week at least.
She will next play the Spaniard Garbine Muguruza, the 2015 runner-up, who breezed through with victory over Sorana Cirstea.
The Spanish 14th seed took just over an hour to record a 6-2 6-2 win against Romanian Cirstea, who was Bethanie Mattek-Sands' second-round opponent when the American suffered her horrific knee injury.
“I’m feeling pretty good,” said Muguruza, who was beaten in the 2015 final by Serena Williams.
“I felt today I improved my game a bit compared to the previous matches. I'm happy the way I'm playing out there.
“It's great to reach the second week. That's everybody's goal, to go through the first week, the first matches, then the exciting part comes now in a way.”
Another former finalist, Agnieszka Radwanska, also made it into the second week of The Championships.
The World No 10 and ninth-seed needed three sets to beat Timea Bacsinszky, who began struggling in the third set with a longstanding thigh problem.
“I had a great match, especially as she's a really tricky opponent,” Radwanska commented after her 3-6 6-4 6-1 Centre Court win.
“I think after the second set I just found my game and I was trying to be more aggressive. I think I was serving as well better in the third set.
“I have been on Centre Court couple of times before, and I really was feeling all the time very good and have playing really good matches. So here, as well, today I think was a great match. When you're there, you're fighting till the last point.”
Coco Vandeweghe, the 24th seed, has yet to drop a set at the Championships after beating fellow American Alison Riske 6-2 6-4 in an hour and 14 minutes.
Vandeweghe has now made it into the second week of Wimbledon for the past two years, and credits the experience of making the quarter-finals in 2015 and the fourth round last year as helping her current campaign.
“Once you have done it once it's easier to do it the second time,” she commented after her win. “I think the first time making a second week of a Grand Slam is probably the most difficult, second to defending it. I think that's a different kind of pressure that is self brought upon.
“I think once you get there, the nerves aren't so anxious, in a way of, you know, can I do this, can I not, because you have already proven it to yourself.”
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