
The 30-year-old, who reached the last eight after Andy Murray retired from their second-round match, did not face a break point against Fritz and will now meet Italian Lorenzo Musetti in the semifinals on Saturday.
“It just goes to show if you stick at it long enough you can keep improving no matter how old you are,” Thompson said.
Musetti moved past British wildcard Billy Harris 6-3, 7-5 to reach his second consecutive semifinal on grass.
American fifth seed Tommy Paul reached his second tour-level grass-court semifinal by beating British hope Jack Draper 6-3, 5-7, 6-4 in just over two hours.
“I played good tennis and I like the grass. I knew today was going to be a battle,” Paul said.
The 27-year-old will face compatriot Sebastian Korda in the other semifinal after the 23-year-old beat qualifier Rinky Hijikata of Australia 6-7(4), 6-3, 6-4 in the last match of the day.