The 37-year-old, chasing a record-equaling 24th grand slam title, came through an intense match to win 6-4 4-6 6-3.
Williams won the last of her seven Wimbledon titles in 2016, but after giving birth two years ago and overcoming a knee injury this season, she looks in ominous form once again.
She will play Barbora Strycova in the last four after the Czech beat Briton’s Johanna Konta 7-6 (7-5) 6-1.
“I believe in myself,” Williams told reporters.
“I believe if I’m feeling well, I can be a big competitor in a sport that I love and I’ve done so well at. So just the key word is getting fit and getting back into match play injury-free.
“So now that I am, I can actually start to play tennis. That has been literally something that I have not been able to do all year.”
Williams continued her winning form later on Tuesday as she progressed into the third round of the mixed doubles with partner Andy Murray.
The high profile duo beat Fabrice Martin and Raquel Atawo 7-5 6-3 in an entertaining match.
Elsewhere, former world No.1 Simona Halep fought back from 4-1 down in the first set against against China’s Zhang Shuai before triumphing 7-6 6-1.