German mother of two Maria regrouped after failing to serve for the match to complete a 6-4, 7-6 (7/4) win.
A single break in the first set put the 37-year-old Maria in charge and she maintained her grip, breaking twice to lead 5-3 in the second.
But Kazakh fourth seed Rybakina, Wimbledon champion in 2022, upped her game to level at 5-5 and the set went to a tie-break.
The players were locked at 4-4 before Maria, ranked 86th in the world, won the last three points, sealing victory with an ace in one hour and 45 minutes.
Maria, who reached the Wimbledon semi-finals in 2022, was forced to qualify for the grasscourt tournament in London.
"It means so much to me," she said. "It's like a perfect example to never give up and to always keep going, doesn't matter what.
"I'm still here and living this dream. I have my family with me and amazing team."
She added: "I'm super, super proud to be here in the semi-final and I hope in a few years you will see my daughter (aged 11) at the same stage here."
Earlier, US second seed Keys came from a set down to beat Russian fifth seed Diana Shnaider 2-6, 6-3, 6-4.
Britain's Emma Raducanu takes on China's Zheng Qinwen later on Friday, with Emma Navarro in action against Amanda Anisimova.