Hidalgo needed two extra holes to beat three-time champion Rahm and claim play-off victory by sinking a two-foot putt after both players had birdied the first.
"Two or three years ago, I was in the first tee, in the trees, supporting Jon - without playing, I just come here to Madrid to see the tournament," said Hidalgo.
"To be here and win the tournament is unreal. Oh, my gosh, it's amazing."
The duo started the day together in an all-Spanish final group with David Puig.
But Hidalgo's two-shot overnight lead evaporated as his group-mates birdied the first hole - which he bogeyed.
The 26-year-old recovered his composure to complete his final round with a score of 70.
When Rahm birdied the 17th and 18th, his final 68 meant the two Spaniards were tied on 14-under, forcing a play-off.
After the pair both birdied the first extra hole, Rahm hit a wayward tee-shot on the second and then chipped through the green.
Hidalgo kept his nerve to nurse the ball close to the pin and then made no mistake from close range to seal his maiden win at his local open.
"May he (Hidalgo) enjoy it," said Rahm.
"Winning at home, winning a Spanish Open with all the support that there has been. You could tell how much he felt it and how important it was for him."