The second-seeded Romanian shaded the early Centre Court exchanges, pouncing on errors and breaking serve to lead 3-0, as the Briton struggled to keep her searing groundstrokes in court.
But with cheers and cries of “C’mon Jo” echoing around the roofed-in arena, sixth seed Konta fought back, cranking up her serve and winning eight straight points to draw level at 4-4.
Halep won the first set on a tiebreak with Konta, having squandered a clutch of break points, returning the favour in the second.
The intensity moved up a notch in the third set as the Briton hit harder and the Romanian tightened her defence, before Konta broke in the fifth game and held her nerve to serve the match out.
Right now it’s a little bit surreal,” Konta told the BBC.
Johanna Konta of Great Britain celebrates victory after the Ladies Singles quarter final match against Simona Halep of Romania on day eight of the Wimbledon Lawn Tennis Championships at the All England Lawn Tennis and Croquet ClGetty Images
“I stuck to my true self and tried to create as many opportunities as possible. I knew she was not going to give much away for free so I definitely had to be the one to create my own chances. I did that and feel fortunate to have taken a few of them.”
On facing the 37-year-old Williams, a five-time Wimbledon champion, Konta said: “Age is not a factor. She’s a tremendous champion and I feel very humbled to share a court with her again.”
Virginia Wade was the last British woman to reach the semi-finals in 1978.
