Rodrigo Freudenthal and Rodrigo Marta had tries for the invitational Portuguese side.
Australia have been beaten 40-19 by New Zealand in their pool showdown at the Hong Kong Sevens, leaving them with an uphill task to qualify for the finals.
Douglas, Canada's all-time try leader, had missed the two previous stops due to a concussion.
The Cheetahs were on the backfoot nearly immediately, as they struggled in defence, allowing Tonga to run in three tries in the first half, while managing one conversion to take a 17-0 lead at the break. Luciano Gonzalez's try early in the second half proved to be enough for the win with subsequent tries by Douglas and Connor Braid leaving Canada just short despite Argentina going a man down with back-to-back yellow cards.
Winger Dan Norton became the leading try scorer in the history of the Hong Kong Sevens on Friday, helping his team beat Wales 36-19 at the format's most storied competition.
But their moment in the sun came in their third and final pool match against Uganda, winning 26-5 to set up a match-up against Japan.
Kazakhstan also still have hopes of reaching the series after winning one of their three pool matches in Hong Kong to reach the last eight, alongside Hong Kong who booked their place in the quarter finals with a 26-5 win over Uganda.
South Africa, who went through Pool "A" unscathed, beating Japan 22-7, Scotland 26-10 and Samoa 21-7, face US in the Cup quarterfinals.
New Zealand have gotten off to the ideal start at the Hong Kong Sevens, trouncing trans-Tasman rivals Australia 40-19 in their opening pool match.
The ladies then beat Papua New Guinea 20-10 in the last pool match to top with nine points.
In the women's qualifying tournament, Brazil beat Scotland 28-19 to win the title.