Kerber, who was runner-up to Serena Williams last year, has struggled for form in recent months and lived dangerously for more than two hours on Saturday before eventually securing a fourth-round place with a 4-6 7-6(2) 6-4 victory.
That Kerber eventually landed safely in the fourth round was more down to Rogers's lack of grasscourt experience than the German suddenly finding her range.
Rogers belted down 48 winners compared with just 25 from Kerber but she was eventually undone by her unforced errors -- the final tally totalling 47.
"She was hitting the balls very hard. I was just trying to find my rhythm," said twice grand slam champion Kerber.
"The key was that I was fighting, and I was never giving up... doesn't matter what the score was. Without this (fight) I don't know if I would be in the next round right now."
Kerber was first thrown off course just three games into the match when a backhand error handed Rogers a break.
The 24-year-old held on to the advantage to pocket the set and repeated the same feat in the third game of the second set.
World number 70 Rogers appeared to have one foot in the next round as she streaked to a 4-2 lead but when Kerber produced a net charging half-volley winner in the eighth game, she was sparked into life.
A forehand error from Rogers handed Kerber the break for 4-4 and from then on the duo were engaged in a battle of wills as they dragged each other into heart-pumping rallies that often stretched to over 15 shots.
Once Kerber won the longest rally of the match, a 21-shot belter from the baseline, she strode 6-2 ahead in the tiebreak.
But as she stood one point away from levelling the match, she stopped dead in the middle of her service motion as a bee buzzed around her head.
Yet the hovering pest was the least of her worries as Kerber desperately tried to overcome a pesky opponent whose stinging groundstrokes were proving to be a continual nuisance.
A backhand winner at the end of a 13-shot rally earned her the second set but the players barely had time to catch their breaths as they were soon engaged in a 10-minute game that stretched to six deuces before Kerber finally converted a fifth break point to go 1-0 up in the decider.
The world number sealed victory when Rogers clubbed a service return long.
She will face 2016 French Open champion Garbine Muguruza on Monday for a place in the quarter-finals.
(Reporting by Pritha Sarkar, editing by Toby Davis and Clare Lovell)
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