The American put his opponent over in the eighth round with a shot on the back of the head and then hit him again when he was on the canvas.
But referee Russell Mora did not give it as a disqualification and Davis remained unbeaten.
Davis did not impress the crowd throughout with his showboating not going down well in the T-Mobile Arena.
The Baltimore boxer had already been stripped of his IBF super-featherweight title after he failed to make weight for the bout.
Davis walked to the ring in bizarre attire that included a huge hood and then his shorts had blue fur down the side.
He was the heavy betting favourite for the clash and expected to cruise past the Costa Rican.
Davis showboated in the fourth round by putting his hands behind his back but he took three clean shots.
The fighter – tipped to be boxing’s next big star – then got dragged into a hard fight.
Davis lashed in body shots in the eighth round but then put him over with a shot to the back of the head.
He then hit him on ground which could have brought about a disqualification but Davis got away with it.
The crowd took it out on him as they booed his interview in the ring and again when the finish was replayed on the big screen.