[3] In his professional debut, on March 1, 1973, Dávila defeated Carlos Villareal in a four-round bout decided on points.
He beat Lupe Pintor by a 10-round decision in 1976,[5] and lost to Wilfredo Gómez by a knockout in Puerto Rico, the first fight in which he was knocked out.
The bout took place in the Louisiana Superdome, and was part of the undercard for a world heavyweight championship fight between Muhammad Ali and Leon Spinks.
[8] After Pintor beat Zarate for the WBC title,[9] Dávila was given a second chance at that belt in a 1980 rematch with the Mexican world champion, and lost by a 15-round decision.
[4] In March 1983, Pintor suffered a motorcycle accident and was forced into a lengthy absence,[11] leaving the WBC bantamweight crown vacant.
The WBC assigned its number one challenger, Dávila, to face its third-ranked fighter, Kiko Bejines, for the interim title.
[1][12] The fight was held in Los Angeles, and most of it was described by Associated Press sports writer Ken Peters as "uneventful".
He returned to the ring two months after the Bejines bout for a fight against Julio Rodrigues in which the WBC title was not at stake.
[20] A title defense was instead scheduled on September 14, 1984, versus Miguel Lora, but in a sparring session two weeks before the fight date, Dávila injured his back.
With 51 seconds left in the round, a doctor stopped the bout due to the cut, giving a technical knockout win to Duarte.
[25] The protest was voted on in July by California's State Athletic Commission; the voters deadlocked 3–3, leaving the result unchanged.
[26] In a bout held at the Great Western Forum in Inglewood, California on November 3, 1987, against Mexico's Juan Estrada, Dávila suffered an accidental headbutt and was given the victory through a technical decision.
[28] After scoring an eighth-round knockdown of Contreras, Dávila narrowly won a unanimous decision; all three judges had him ahead by either one or two points.
Los Angeles Times columnist Jim Murray called Dávila "a picture boxer", saying that he fought "with his brains instead of his face.
"[6] Murray credited Dávila's style to his childhood gym experience, when he discovered that he could avoid being punched if his opponent made the first move.