Parker, who came to the ring wearing a Manu Samoa/All Blacks tribute jersey celebrating the recent test in Apia, will next fight in Auckland on October 15.
The fight was not only very well received in Invercargill, with a capacity crowd, it was also Parker's highest rating pay per view fight. He's moving up in terms of profile and reputation, and this victory will likely put him among the top five heavyweights in the world.
Tupou went on the attack from the opening bell, as expected. He swung with both hands and it appeared to rattle Parker, who took a few moments to find his feet, but the response was impressive.
"We knew he was going to come for it," Parker said. "He wasn't going to try to box me. I have a height and reach advantage and I knew he was going to come strong and we were prepared for it."
He added: "I took the opportunity and threw an overhand right which landed on his temple. I felt it connected real well and when I looked down he was on the ground.
"It only went one round and we were prepared to go 12, but we're happy with the victory.
"We prepared well. We worked on my defence but we didn't get a lot of rounds to show it."
Parker, who conducted his press conference with a pottle of Bluff oysters in one hand and a burger in the other, will create a stir with the manner of this victory.
He now holds four belts - including Tupou's WBO Africa heavyweight title, and, while he was always expected to be too fast and skilful for the 32-year-old, who trained under three-time world champion Jeff Fenech, the finish was spectacular.
Barry said: "I still go back to two and a half years ago when the media and some people in New Zealand said Joseph Parker can't punch. I think everyone knows now that he hits as hard as any heavyweight in the world. I'm damn sure that fight being on ESPN and being seen by a lot of people around the world and with Joe's growing profile that we've sent some more shudders through the division."
Barry and Parker are targeting a world title shot in the next 18 months to two years.