Rodrigo Freudenthal and Rodrigo Marta had tries for the invitational Portuguese side.
The Hong Kong Sevens continues this weekend, live on Sky Sports Action, with England seeking to continue their good start against Spain and USA.
Japan threatened an upset as they still led early in the second half, but a try by Werner Kok put the Blitzboks in the lead, and two more tries by Justin Geduld and Siviwe Soyizwapi sealed the deal for South Africa.
The Canadian men open play on Saturday against France before taking on Portugal.
Norton, who leads the circuit with 324 career tries, broke the record set by Collins Injera of Kenya at the 2017 tournament.
Fiji defeated Kenya 22-5 in their first pool match of the Hong Kong 7s last night.
England moved into second place in Pool D with the victory.
In other matches, Samoa beat Scotland 17-7, South Africa defeated Japan 22-7, England beat Wales 36-19, United States of America defeated Spain 36-7 and New Zealand thrashed Australia 40-19.
South Africa, who went through Pool "A" unscathed, beating Japan 22-7, Scotland 26-10 and Samoa 21-7, face U.S. in the Cup quarterfinals.
New Zealand will battle Kenya at 4.51 this afternoon.
Fiji will now take on Australia at 5.13pm today and play their final pool match against New Zealand at 8.55 tonight.
In the women's tournament, Brazil beat Scotland 28-19 to win the title.