The 23-time Grand Slam champion dropped her first set of the championships but came through 3-6 6-3 6-4.
Ostapenko was more efficient, serving her match out at love and converting her first match point with her 14th backhand victor.
In March, she lost in the first round of the Miami Open to Naomi Osaka, leading to a hasty exit in which she bypassed a postmatch media session.
Yet here Williams is, getting stronger and moving better with every match. In a tournament where the top 10 women's players have been eliminated, Giorgi hadn't faced a seeded player since her first-round win over No. 21 Anastasija Sevastova. As you may have seen from my comment on the previous post I was lucky enough to watch this one live on Centre so this is a slightly different format here as I didn't take any notes to do a quick match recap but my thoughts are Fed looked top class.
Williams, a 23-time major victor, is hoping to join a select group of women who have won Grand Slams after becoming mothers.
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"The seas have parted for her", nine-times champion Martina Navratilova said from the BBC's courtside bunker. "You really can't have a weakness against Serena". "This is only my fourth tournament back", she said. "Everybody has the same chances to win that match, and I'm looking forward to it". "I went for it", Serena said.
The 36-year-old will play German 13th seed Julia Goerges on Thursday for a place in Saturday's final boasting a 3-0 career record. Bertens is seeded 20th.
Her star power grew during a match against Serena Williams in the quarterfinals when she won the opening set and challenged in the third. She had never even got to the quarter-finals of a major tournament before, let alone the semi-finals.
Williams was seeded 25th by the All England Club, a nod to all of her past success at the grass-court major, including titles the last two times she entered it, in 2015 and 2016.
Next up for Kerber is Russian 14th seed Daria Kasatkina, who took out Belgian Alison Van Uytvanck 6-7 (6-8) 6-3 6-2. If she missed her first serve, she'd simply blast another first serve with all her might, rather than a high-percentage second serve, and not worry about double-faulting.