Herbert, ranked 93rd in the world, won 6-7, 6-4, 6-2 in just over two hours to claim his first victory over a player in the top five.
Tsitsipas, 22, who had been seeking a third consecutive title at the tournament, edged the first set.
But from 4-4 in the second set, it was one-way traffic as Herbert raced to the net to finish points and then matched the Greek in exchanges from the baseline.
"I knew I was going to have to play an amazing match to have a chance to win," said Herbert after the success.
Effort
"And I managed to do that. I am really happy about the way I played. I am so happy to be in the semi-finals here.”
Pierre HUGE WIN Herbert 🇫🇷@p2hugz beats two-time defending @Open13 champ Tsitsipas 6-7 6-4 6-2 to reach the last four - his first win over a top 5 player! pic.twitter.com/VrQL3HWhaR
— Tennis TV (@TennisTV) March 12, 2021
Herbert will take on one of his compatriots - Arthur Rinderknech or Ugo Humbert - on Saturday for a place in Sunday’s final.
“That's good that there is going to be a French player in the final,” said Herbert. “I am happy about that and I hope it is going to be me.”
Top seed Daniil Medvedev, the Australian Open finalist, will take on the qualifier Matthew Ebden in the other semi-final.
Medvedev overpowered the fast rising Italian Jannik Sinner 6-2, 6-4 while Ebden came from a set down to see off Medvedev’s fellow Russian Karen Khachanov 4-6, 6-4, 6-2.
