The Wimbledon champion converted five out of seven break points to secure the victory and set up a last-four clash with unseeded Ons Jabeur.
"I am really happy how I played," Kerber told the BBC. "To play against Simona, you know you have to play the best tennis."
Tunisian Jabeur was made to work hard for a victory over Alize Cornet as she shook off an ankle injury in the final set to prevail 1-6 7-5 6-3.
"At this tournament, I'm the queen of losing the first set and then coming back," Jabeur, who has rallied back from a set down to win three of her four matches in Eastbourne, said.
"It's another motivation for me to win, to play better in the second set, but I'm really happy with this win.
"It wasn't easy at the end, I was scared for my ankle, but hopefully everything will be good. I tried to move better, be better on court, and that helped me regain my shots."
Kiki Bertens survived a mid-match wobble to extend her dominance over world number 10 Aryna Sabalenka, beating last year's runner-up 6-4 3-6 6-4.
The St Petersburg and Madrid champion's fourth victory over Sabalenka in as many career meetings took her to a seventh semi-final of the year, where she will meet former world number one Karolina Pliskova.
Czech Pliskova fired 22 winners and sent down six aces to down Russia's Ekaterina Alexandrova 6-2 6-0.
"I'm improving with every match here," Pliskova, who is yet to drop a set in the tournament, said.
"I was hoping to get some matches here before Wimbledon and I won three matches against solid players... I'm in the semis for the third time... it's going to be a good challenge for me (against Bertens)."
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar and Ed Osmond)
