In a testament to her remarkable longevity, the former world number one has now made at least one Grand Slam final for the last 12 years.
The Latvian trailed 3-0 and 5-4 before rattling off nine of the final ten games in the match to advance to her second straight quarterfinal at the All-England Club where she will face Dominika Cibulkova.
Meanwhile, 2017 French Open champion Ostapenko made light work of Cibulkova who hadn't previously lost a set throughout her Wimbledon campaign.
Serena Williams will play in her 35th Grand Slam semifinal against an opponent appearing in her first.
Jelena Ostapenko became the first Latvian woman to reach a Wimbledon semifinal with a 7-5, 6-4 victory over Dominika Cibulkova.
Rebounding from her shock first-round elimination in her Roland Garros title defence, Ostapenko has marched through the draw without dropping a set. If there is one lesson I would teach my daughter it's never giving in, always fighting.
Kerber had this year shown great signs of regaining the form and confidence that slipped in the aftermath of her breakout 2016.
And on Tuesday, she booked her spot in the semi-finals at SW19 in typically calm fashion.
The 36-year-old Williams was absent from the All England Club in 2017 due to her pregnancy, and played her first Grand Slam since giving birth at the French Open last month when she reached fourth round. She produced 33 winners in total to Cibulkova's six and was pure box office for all 88 minutes of her 7-5, 6-4 victory. "I'm going to go out there and just do what I can, do my best, see what happens".
"It was a really tough match and I was just trying to enjoy it", Ostapenko said. Daria Kasatkina played her part, but Angelique Kerber had the final say. But I'm going to prepare well for it, going to be probably long rallies.
"I had no sympathy because it's just about the chair umpire". She delivered three aces to the American's one in the first set and won 84% of points on her first serve. Dreams can quickly turn to nightmares on a tennis court, so the strategy meeting that Goerges had planned with her team for Wednesday was set to be crucial. I was not thinking too much about the match points.
The seven-time champion, who missed the tournament past year, was outplayed by Italian Camila Giorgi in the first set but rallied to win 3-6 6-3 6-4 on Centre Court.
"It's my point", Cibulkova said, ignoring the fact she had stopped before Hseih's shot legally landed in.
For the first time in the Open era, not a single top 10 seed has made the quarter-finals at one of the four Grand Slams.Kerber beat Kasatkina on grass at Eastbourne two weeks ago and again she was in control, finishing off the first set easily before landing an early break in the second.
Kerber again broke to go 3-1 up in the second set before Kasatkina levelled for 3-3 only for another double fault to put Kerber back in the driving seat.