A Renee Holmes penalty would be the only other points in the second, as Manawa took an 8-0 lead at halftime.
Laura Bayfield struck back for the visitors just sixty seconds after the break, Maia Joseph scooting from the base and linking with her lock looming on her inside.
Winger Reese Anderson replied just two minutes later, and just as Manawa looked to be taking control of the contest, Winnie Palamo bagged a stunner.
Fullback Kaea Nepia exploded through the line and busted through several would be tackles on a superb run, eventually finding her right winger to finish off the breathtaking break.
Matatū then took the lead courtesy of a powerful straight run from Amy Du Plessis as she went in right next to the sticks.
Manawa weren’t done though, skipper Kennedy Tukuafu rumbling her way over, Holmes spraying the conversion to keep the margin at four with ten to play.
Du Plessis’s second all but sealed the deal, having been denied moments earlier, the centre again proving too strong close to the chalk.
Tui pulled one back for the hosts to set up a grandstand finish, Manawa deep inside their own territory as they fought to find an opening, but it proved a hurdle too far and Matatū closed out a pulsating season opening victory.
In the second game of the day, the Blues women put Hurricanes Poua to the sword with a 50-10 win, running in seven tries in Wellington.