Left-handed Quiroz, world 276, pulled the upset with big serves that kept 90th-ranked Uchiyama on defensive.
He nailed 16 aces and won points on 78 percent of his first serves. Uchiyama came back in the second set by breaking Quiroz twice and mixed his sizzling forehand shots with delicate volleys to force his opponent to make mistakes.
But Quiroz stayed in the match, with both men keeping all of their service games in the first and third set, with the Ecuadoran overcoming Uchiyama in tie-breaks after the two sets.
Gomez, ranked 151, also stayed in control of his match against 117-ranked veteran Soeda.