The Finn Valley fighter won the fight after three rounds with a TKO.
Jason was always on the front foot and in the third round he left Najara bloodied after a flurry of punches.
The Mexican didn't come out for the fourth round with his corner signalling he couldn't continue.
The fight was part of the undercard of the Kell Brook / Shawn Porter world title bout where Brook stretched his perfect record to 33 straight wins.
For Quigley, it was another step on the professional ladder - after the fight he spoke with Chris Mc Nulty.