Chris Coleman's unheralded outfit bounced back from Radja Nainggolen's fine 13th-minute opener to level through Ashley Williams and then streak clear with Hal Robson-Kanu and Sam Vokes goals that bookended a scarcely believable second-half story.
It was Belgium who had begun this remarkable game writing history, 21-year-olds Jason Denayer and Jordan Lukaku making Marc Wilmots's team – average age 24 years and 242 days – the youngest starting XI at a EURO since 1968.
A bright opening reflected these bright complexions. Wayne Hennessey blocked from Yannick Carrasco, Neil Taylor from Thomas Meunier and James Chester from Eden Hazard. There was no getting in the way of Nainggolan's 13th-minute thunderbolt, his second goal of the finals.
In reply Gareth Bale ruffled the side netting and Thibaut Courtois saved from Neil Taylor. Captain redoubtable Williams made the third attempt count, bullet-heading Aaron Ramsey's corner. At 1-1, Bale, Ramsey and Williams all threatened.
Both countries wanted to improve on 1-0 defeats in their previous quarter-final outings – Belgium's 2014 reverse to Argentina, Wales's loss to Brazil 58 summers ago. Romelu Lukaku and Eden Hazard nearly helped achieve this soon after half-time. However, both men were off target and, with a splendid strike that was half his invention and half Ramsey's, Robson-Kanu wasn't.
Williams's scissor kick underlined the underdogs' burgeoning confidence. Marouane Fellaini might have put a dent in it with two headers – the second almost falling for Axel Witsel. Instead the head of substitute Vokes, from Chris Gunter's cross, conclusively denied Belgium a first EURO semi-final since 1980 and sent Wales into dreamland.
Man of the match: Hal Robson-Kanu (Wales)
Support Our Journalism
We cannot do without you.. your contribution supports unbiased journalism
IBNS is not driven by any ism- not wokeism, not racism, not skewed secularism, not hyper right-wing or left liberal ideals, nor by any hardline religious beliefs or hyper nationalism. We want to serve you good old objective news, as they are. We do not judge or preach. We let people decide for themselves. We only try to present factual and well-sourced news.