Parodi, who had only lost once in 37 outings before the weekend, dropped to one knee for respite after being caught with a left to the body one second from the end of sixth and failed to beat the count.
Unbeaten Frampton was the dominant force throughout and had stunned the Frenchman with a right uppercut in the fifth.
The ex Irish Elite champion, who is managed by Barry McGuigan, improves to 17 wins after the KO that saw him retain his European and IBF Inter-Continental titles.
McGuigan wants to offer either Spain’s Kiko Martinez, who Frampton beat at the Odyssey Arena last February, or South Africa’s Jeffrey Mathebula a huge payday in Belfast.
Martinez defends the IBF belt against Mathebula, the mandatory challenger, in Alicante in December and Frampton will be directly in line to meet the victor.
“We will do everything possible to bring that fight to Belfast. Carl Frampton will win a world title, if not in his next fight, then the one after that,” insisted McGuigan. “We can put a package together that will persuade Martinez or Mathebula — whoever wins — to come to us.”
Frampton added: “I am the hardest punching super-bantamweight in the world. I knew Parodi wouldn’t be able to stand my power and that it was only a matter of time before I’d break him down. Obviously, I’d love a world title shot straight away, but with Martinez and Mathebula not meeting for another two months, I probably will get in another fight before meeting the winner.”
Meanwhile, Ryan Burnett stopped Nicaragua’s Reynaldo Cajina in the second on Saturday’s undercard. Jamie Conlan, a brother of London 2012 bronze medalist Michael, stopped Argentina’s Walter Rojas in the first and Marco McCullough TKO’d Willie Casey to claim the vacant Irish featherweight title.