It's the third event in a row that the Canadian men have made the final eight of the elite Cup competition.
The Canadians went 2-1-0 Saturday at the finale on the nine-stop HSBC Sevens World Series. They will play the United States on Sunday in the quarter-finals.
Canada, which came into the tournament 11th in the standings, beat No. 9 Samoa and No. 8 Argentina before losing 31-14 to Series leader Fiji.
A marquee quarter-final matchup sees Fiji plays No. 2 South Africa in a game that will decide the overall series winner.
The other men's quarter-finals are New Zealand versus England and Australia versus Scotland.
The Fijians, whose career record is 39-2 against Canada, scored off the opening kickoff and sliced open the Canadian defence several times en route to a 21-7 halftime lead. Adam Zaruba crashed over the line on the final play of the half to put Canada on the board.
"One more score, game over," Fiji coach Ben Ryan told his team at halftime.
That came less than a minute later as Fiji intercepted a pass near its goal-line and scored on the ensuing attack.
Nathan Hirayama added a try for Canada and Harry Jones kicked two conversions.
The Fiji win meant the Pacific Islanders went through the entire season without losing a game in pool play, winning 27 straight.
The tournament, officially called the Marriott London Sevens 2015, drew a record crowd of 77,033 to Twickenham Stadium with many in costume. Organizers called for a galactic fancy dress theme. following last year's successful monster motif.
In beating Brazil 56-7 to also advance to the Cup quarter-finals, England secured Olympic qualification for Team Great Britain at the 2016 Games.
The top four teams in the final standings automatically qualify for the Olympics with No. 1 Fiji, No. 2 South Africa and No. 3 New Zealand having already booked their ticket. England came into the London tournament fourth in the table.
Canada will look to a regional qualifier in June when they will likely have to beat the U.S. to qualify for Rio de Janeiro. The loser will get one last chance via a world repechage.
The Canadians have played the U.S. four times on the circuit this season, losing three times. But they beat the Americans 40-0 last week in Glasgow.
The U.S., who have made six quarter-finals this season and currently stand sixth, upset South Africa 14-12 Saturday, a result that set up the Sunday showdown with Fiji for the Blitzboks.
Japan, 15th in the standings, led New Zealand 14-12 at halftime before normal service resumed with the Kiwis winning 26-14. The Japanese lost all three of their matches Saturday, which confirmed their relegation. They will be replaced by Russia in the 2015-16 series.
Canada opened the day with a 17-14 win over No. 9 Samoa thanks to tries from Sean Duke, Hirayama and Jones, who added a conversion.
The Canadians then turned it up a notch, avenging a loss to Argentina last week in Glasgow by beating the South Americans 26-5. Hirayama had two tries with singles going to Mike Fuailefau and Conor Trainor. Jones kicked three conversions.
Canadian coach Liam Middleton had to summon Connor Braid (Glasgow Warriors) and Matt Evans (Cornish Pirates) ahead of the weekend tournament after losing Liam Underwood and Ciaran Hearn to injury.
Underwood suffered a head injury and Hearn hurt his ankle in Glasgow, where the Canadians tied for seventh. Canada placed fourth at the previous tournament in Tokyo.
The Canadians finished sixth in the 2013-14 World Series standings.