The Netherlands struck two second-half goals in seven minutes to come from behind to beat Turkey 2-1 on Saturday and set up a Euro 2024 semi-final clash with England.
Samet Akaydin sent Turkey ahead in the first half but Stefan de Vrij headed the Netherlands level and Murt Muldur turned into his own net under pressure from Cody Gakpo after 76 minutes to hand the Dutch victory.
The build-up to the quarter-final clash in Berlin was overshadowed by a diplomatic row between Turkey and Germany after their last-16 hero Merih Demiral was banned for two matches for making a controversial salute.
Turkish President Recep Tayyip Erdogan attended the match at the Olympiastadion as a result, along with tens of thousands of fans who greeted every sustained Dutch period of possession with a barrage of whistles.
Netherlands overcame the pressure from the stands and Turkey's energetic style, as well as a flurry of late chances, to reach the Euros semi-finals for the first time since 2004.
"Tonight we had to dig very deep and I am proud of these guys," Netherlands captain Virgil van Dijk told NOS.
"We made a very good start in my eyes (but) we got sloppy and lost balls at dangerous moments... then we had to try and stay calm and take advantage of the chances that were going to come...
"We want to fulfil our dream and we are one step closer."
Turkey coach Vincenzo Montella deployed five at the back, hoping his young side could catch Netherlands on the counter-attack.
It was the 1988 Euros champions who carved out the first chance, with Gakpo and Memphis Depay linking up well before the latter blazed over.
Koeman captained the Netherlands to glory 36 years ago but until their convincing 3-0 win over Romania in the last 16, the Dutch looked incapable of challenging for the trophy, sneaking through their group in third place.
They reverted to that weaker self in the first half after their early incursions, allowing Turkey to firmly establish themselves in the game.
Montella's side began to pin the Netherlands back with a string of set pieces, eventually capitalising after 35 minutes when Arda Guler recycled a corner which was only half-cleared.
The 19-year-old Real Madrid playmaker swirled in a cross dripping with temptation with his weaker right foot, and Akaydin, who returned from suspension to replace the banned Demiral, powered home a far post header.
Turkish fans, unsurprisingly filling three-quarters of the stadium given their large diaspora in Germany, roared and ignited flares in celebration.
- Weghorst the game-changer -
Koeman had to shake things up at the interval and brought on Wout Weghorst, the team's saviour against Poland in their opening fixture, for Steven Bergwijn.
The burly Burnley striker made a rapid impact, giving the Netherlands a target to hit up front, which they looked for with regularity.
Guler continued to probe at the other end and was scythed down by Nathan Ake, crashing the resulting free-kick against Bart Verbruggen's post.
Turkey, in their first quarter-final at a major tournament since 2008, almost grabbed a second but Verbruggen saved well from Kenan Yildiz.
At the other end Weghorst forced a smart stop from Mert Gunok, but the Turkish goalkeeper was soon beaten by De Vrij.
Memphis Depay swung in a cross after a short corner and Inter Milan defender De Vrij met it with a towering header to level in the 70th minute.
Just six minutes later, Denzel Dumfries swept in a dangerous low ball which Muldur bundled into his own net as Euros joint-top scorer Gakpo tried to reach it. It was the 10th own goal of the tournament.
Although Weghorst was not directly involved in either goal, his presence in the box completely unsettled Turkey's previously sturdy defence.
Montella's side should have levelled but Zeki Celik and Kerem Akturkoglu had efforts blocked in a frantic finale and the Netherlands lived to fight another day -- against England on Wednesday in Dortmund.
Turkey substitute Bertug Yildirim was sent off for dissent from the bench in the final stages, ensuring his country matched the worst ever discipline tally in Euros history -- 19 yellow cards and one red, set by the Czech Republic in 1996.