The Dutch trailed at half-time in their quarter-final in Berlin before a second half header from Stefan De Vrij and a Mert Mulder own goal turned the game on its head.
They will now play England, featuring City trio Kyle Walker, John Stones and Phil Foden in the second semi-final after Rodrigo’s Spain play France.
While the Dutch were patient in their build-up in the last of the quarter-finals, Turkey’s speed and directness in the first half caused them problems and they deservedly took the lead in the 35th minute.
Arda Guler’s pinpoint far post cross picked out Samet Akaydin who powered a header past Bart Verbruggen.
Turkey kept pushing for a second Real Madrid winger Guler almost doubled their advantage after the break with a powerful low shot that clipped the outside of the post.
Verbruggen then made a reaction save from Kenan Yildiz and striker Wout Weghorst stuck out a long leg to scramble the ball clear.
And they were made to pay for missed chances as the Dutch scored twice in the space of six minutes.
De Vrij rose unmarked to emphatically head home Memphis Depay’s cross before a low centre was turned in by Mulder at the back post under pressure from Cody Gakpo.
Turkey pushed hard for an equaliser with Virgil Van Dijk and Micky Van de Ven making blocks from goalbound efforts.
And when Semih Kilicsoy was on the end of a deep ball into the box, Verbruggen reacted brilliantly to push the ball away.
England will now play Netherlands on Wednesday 10 July at 20:00 (UK) in their first European Championship encounter since the Three Lions won 4-1 at Wembley in 1996.
And the reward for the winner will be a place in the final to face either Spain or France who meet in the other semi-final 24 hours earlier.
