In a match dripping with tension towards the business end of one of the most open women's grasscourt grand slams in years Konta rode a wave of home support to win 6-7(2) 7-6(5) 6-4.
The sixth seed and second-seeded Halep were facing each other for the first time since a turbulent Fed Cup tie in April.
Serving up the only tennis show in town as the rain drummed down outside the roofed-in Centre Court and avoiding eye contact at changeovers, the pair also had the extra weight of history to contend with.
Konta, working hard to keep her opponent pinned behind the baseline, was bidding to book a date with Venus Williams on Thursday as the first home semi-finalist since Virginia Wade in 1978, the year after Wade won the title.
Halep, scampering from wing to wing as she soaked up the pressure, was one match from becoming the first Romanian to top the computerised world rankings - a distinction that, following her defeat, passed to Czech Karolina Pliskova.
The refined surroundings of the main showcourt were a world away from the tiny stadium on the Black Sea where the two players last met, Halep winning that encounter in straight sets.
Konta became tearful during her other singles match in that Fed Cup tie, against Sorana Cirstea, blaming what she called a hostile reception from Romanian fans who Halep this week described as "very fair".
On Tuesday the Australia-born Briton struggled to take it all in too -- but for altogether different reasons.
"Right now it's a little bit surreal," she told the BBC after sealing victory in just under two-and-three-quarter hours.
"Simona... was really not going to give me much for free so I definitely had to be the one out there to create my own chances and I felt I did that."
Konta said she was "excited and humble" to be facing Venus Williams, a match that Wade predicted the Briton would win.
"It’s fine to be the last British women’s winner (at) ...Wimbledon, but it’s better to have plenty of British players to win," Wade said in comments released by the All England Club.
"If I get a chance I will tell (Johanna) how well she played and wish her good luck."
FINAL SCREAM
The match closed on a surreal note, when the final point was punctuated by a spectator's scream, Halep lamely netting a forehand as she appealed in vain for a let.
In a nod to that episode, Konta described the crowd as incredible, adding: I think they were a little over-enthusiastic in parts, but I definitely cannot complain with the amount of support and general good feeling they were wishing my way."
Defying the cheers and cries of "C'mon Jo" echoing around the arena, where only the Royal Box had seats to spare, Halep shaded the early exchanges.
She pounced on any error and broke serve to lead 3-0 as the sixth-seeded Briton, close to brimming over with nervous energy, struggled to keep her searing groundstrokes in court.
But 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 before Konta broke in the fifth game and held her nerve to serve the match out.
The stadium erupted and, out on Henman Hill, the umbrellas of the fans massed in front of the big screen twirled.
"We've been to every (other) Konta match," said Glenda Powell from Farnham. "She gives the British people heart."
(Reporting by John Stonestreet; editing by Ken Ferris)
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