The Canadians defeated Portugal 40-5, played Wales to a 17-17 draw, and lost to New Zealand 22-17 to move on to the elite Cup portion of the competition.
"We are very pleased to make it three straight Cup appearances," said Canadian coach Geraint John. "I think we are playing well and with confidence as was shown in all three games. Getting into the top eight is important for us and it has shown how we have developed. Two years ago, we were not even a core team. Now we are competitive against all teams."
Canada will face England on Sunday, a team John said is "very fast and skillful, and again it will be a test for us."
Canada started off their Tokyo campaign with an impressive win over Portugal with two tries from Nathan Hirayama and one apiece from Sean Duke, Ciaran Hearn, Harry Jones and Sean White.
A last-ditch try from Jones salvaged a draw for Canada against Wales. Conor Trainor and Mike Scholz also scored in that game.
John Moonlight scored three tries in Canada's loss to New Zealand, the IRB Series leaders.
New Zealand, England and South Africa won all three of their matches to top their respective pools and reach the quarter-finals.
England edged Australia 24-21, adding to comfortable wins over Spain and Scotland.
New Zealand beat Portugal, Wales and Canada and will face Australia on Sunday. The other quarter-final matchup is Fiji against Kenya.
South Africa beat Argentina 28-12 and also cruised by Japan and Kenya. The South Africans will face the United States, which secured its first quarter-final berth of the 2013-14 series by finishing second it its pool.
— With files from The Associated Press.