The 25 year-old Mexican claimed the vacant WBO NABO featherweight belt by beating up and breaking down the former IBF title holder.
Punishing shots early in the fight had left Gradovich a bloody mess, and when the Russian went down hard in the fourth, Russel Mora had seen enough and ended the contest.
Earlier, Freddie Roach protege Jose Ramirez continued his progress with a unanimous ten-round decision win over a stubborn Manny Perez.
Ramirez had too much accuracy and punch variety for Perez and moves to 17-0 in the paid ranks with another step up the ladder.
Oleksandr Gvozdyk made it ten straight wins with a stunning second round knockout of former world light heavyweight title challenger Nadjib Mohammedi.
A crushing straight right hand did the damage as the Robert Garcia-trained Ukrainian recorded an eighth career stoppage.
Welterweight Konstantin Ponomarev improved to 30-0 as a professional and in the process ended a similar unbeaten run acquired by Brad Solomon.
The young Russian, 23, claimed a split decision following ten pulsating rounds as judges carded 98-92, 96-94 in his favour and 94-96 to Solomon.
Also on the off-TV bill, German super middleweight prospect Leon Bauer won 59-55 twice and 60-54 after six rounds to beat Ilshat Khusnulgatin on his American debut, whilst Egidijus Kavaliauskas scored a shutout 80-72 win over Deniz Ilbay at welterweight. Kavaliauskas is now 13-0 as Ilbay drops a first loss in sixteen.
In a four-round swing bout, home fighter Devin Haney made it to 4-0 with a convincing victory over Rafael Vasquez.
