Singles wins for Botic van de Zandschulp and Tallon Griekspoor sparked a party amongst the orange-clad Dutch fans inside the Jose Maria Martin Carpena Arena.
They will face either defending champions Italy or Australia in Sunday's final.
Van de Zandschulp, the player who ended Spanish great Rafa Nadal's career on Tuesday, held his nerve to beat Daniel Altmaier 6-4, 6-7(12), 6-3, although he required 10 match points to give his side the edge in the semi-final.
Germany's Jan-Lennard Struff looked like keeping his side in with a chance of reaching the final for the first time since 1993 as he led by a set and a break of serve against Griekspoor.
But Griekspoor produced a stunning fightback to win 6-7(4), 7-5, 6-4, sealing the decisive win with his 25th ace.