There were no problems for top seed and hometown favourite
Keothavong had a break point in the opening game against Kerber and then took the set with a break in the final game after having earlier saved a break point.
Both serves seemed to breakdown in the second with only three holds in the entire set but Kerber eventually toughed it out to level the match.
The German then just needed the one break in the third to win the match in just under two hours and set up a quarter-final clash with countrywoman and sixth seed Mona Barthel who booked her spot in the last eight on Wednesday by beating Alberta Brianti.
British number two Keothavong will now next be seen in action for the British Fed Cup team who take on Sweden in the World Group II Play-offs in Boras next weekend.
Wozniacki's reward for her victory is a quarter-final tussle with dangerous Frenchwoman Alize Cornet.
Meanwhile, third seed