The Colombian struggled at first in windy conditions and fell behind 4-0 in the opening set before settling into his game, while Young tired and succumbed to 65 unforced errors.
Young had dominated the opening games with a strong serve and heavy forehand, allowing Falla only three points on serve in the first four games.
But Falla improved quickly, recovering to 5-4 before ultimately losing the first set, then staying unbroken in the second and third sets while Young's serving declined.
"I'm very happy that I could get there. It was a very tough day to play because it was very windy," the 74th-ranked Falla said.
"It made it very difficult for both of us. He played well in the early games, but I concentrated on moving my feet more and started to get more confident in my game.
"We both made a lot of unforced errors, which is normal in windy conditions, but I'm very happy with the way I played."
The 22-year-old Young, who lifted his world ranking from 129 to 39 in 2011, gradually lost belief in his aggressive playing style as the errors mounted. He lost serve in the third game of the second set and again in the ninth game to give up the set in 42 minutes.
The left-hander then lost the deciding set with a single service break in the eighth game.