Conceding two late tries, Canada fell 21-19 to Fiji in its final match Sunday. England won the event, beating South Africa 21-14 in the final.
Canada's performance moved Liam Middleton's team up two places to No. 11 in the series standings after sevens stops of the nine-event season.
South Africa won Pool C with a 3-0 record Saturday but Canada also advanced as the best of the other three 1-2 teams on points differential.
That set up a Cup quarter-final showdown Sunday with the powerful All Blacks, who had won all 28 previous meetings between the two.
Canada trailed 5-0 within 20 seconds when New Zealand's Joe Webber scored from the kickoff. But Sean White's offload set up a tying try from Mike Fuailefau before Tim Mikkelson scored to put New Zealand ahead going into halftime.
Captain John Moonlight and Conor Trainor scored second-half tries, with conversions from Harry Jones giving Canada a 19-10 lead that withstood a late Sherwin Stowers try for a 19-15 win.
Canada lost 14-5 to England in the Cup semifinal before falling to Fiji in the battle for third place at Prince Chichibu Memorial Ground.
Trainor scored Canada's lone try against an English side reduced to six men in the third minute when captain Tom Mitchell was shown a yellow card for an alleged punch.
Against Fiji, Canada led 19-7 after 11 minutes on the strength of tries by two tries by Moonlight and one by Ciaran Hearn, with two Jones conversions. But converted tries by Osea Kolinisau and Savenaca Rawaca gave the Pacific Islanders the win.
Despite its best finish of the season, Canada finished with a 2-4 record in Tokyo.