The 25-year-old had not fought since beating Rendall Munroe last year, but is plotting a route to a world title after his latest victory.
Quigg countered his opponent's quick start, working behind his jab before bringing his powerful right hand in to play.
He dropped Prado at the end of the second before working the body in the third and finishing the Brazilian off.
"He's never been stopped before," Quigg told Sky Sports News afterwards. "He;s tough but I don't think he'd ever been hit that often.
"I broke him down in three round basically. I think I was punch-perfect - tell a lie I got caught with a flush jab - but pretty much punch-perfect.
"I've improved so much since the Munroe fight. I've been inactive in the ring but been working hard in the gym."
The win means that Quigg improves his record to 26 victories and no defeats.