Weaver and Poje, who were first after the short dance, won the free dance on Sunday to finish with a total of 169.42 points and claim their second Grand Prix series title following a win at Skate Canada.
"We're very happy, it's our first NHK title," Poje said. "We were happy with our performance today but we made a couple of mistakes that we definitely want to fix before the GP Final."
Ksenia Monko and Kirill Khaliavin of Russia were second with 152.54 points followed by Kaitlin Hawayek and Jean-Luc Baker of the United States with 146.41 points.
Weaver and Poje, from Waterloo, Ont., earned a berth at the Dec. 11-14 Grand Prix Final in Barcelona. Madison Chock and Evan Bates of United States, plus Gabriella Papadakis and Guillaume Cizeron of France previously qualified.
Third-placed Hawayek and Baker won the ice dance title at the Junior World Figure Skating Championships in March and are competing in their first season at the senior level.
"We're thrilled because its only our second Grand Prix in our first year of senior competition," Baker said. "We just wanted to get our name out there with a podium finish and were able to do that."
Alex and Maia Shibutani of the United States also qualified for the GP Final along with Piper Gilles and Paul Poirier of Canada and Russians Elena Ilinykh and Ruslan Zhiganshin.