The 27-year-old Brit dominated Saturday night's bout after stepping up in weight, his Australian opponent taking a lot of punishment before being overwhelmed at the London Olympia.
In what was his first fight at the 168-pound limit, the son of boxing legend Chris Eubank claimed the win following a strong uppercut in round 10.
"His skull was very hard - it was like hitting concrete," Eubank told reporters after the bout.
"I'm coming for everybody, [James] DeGale, I want the rest of those teeth. Of course I want [Gennady] Golovkin, [Billy Joe] Saunders... We have the platform, let's get these fights going!"
Eubank's victory over Quinlan was his 24th from 25 fights.