The Blitzboks and Fijians came into the competition, the penultimate stop on the nine-event HSBC World Series circuit, 1-2 in the overall standings.
The top four in the table at the end of the season qualify automatically for the 2016 Olympics, which marks the debut of the rugby sevens at the Games. The World Series wraps up next weekend in London.
Ironically, Fiji and South Africa will square off in semifinal action Sunday. Fiji has won two of their three meetings this season.
Fiji, which has won three the seven tournaments so far, swept its pool in style, beating Wales 40-17, Portugal 49-12 and host Scotland 45-5.
South Africa rallied from a 5-0 deficit to beat Kenya 22-5, then clinched an Olympic berth when New Zealand came back from a 19-0 deficit to beat Samoa 26-19.
New Zealand, the defending series champion and defending Glasgow champ, put a slight dent in South Africa's celebrations by winning their pool match 24-19, controlling play for the most part.
New Zealand can also qualify for Rio by reaching the semifinals Sunday at Scotstoun Stadium. The Kiwis will have to go through Scotland.
Canada, last year's finalist, also advanced to the quarter-finals for the second straight tournament and will play England on Sunday. The Canadians opened with a bang, thumping the United States 40-0.
Liam Middleton's team fell 21-12 to Argentina before beating Japan 38-0 to win its group and advance to the final eight of the Cup competition.
The Americans rallied to beat Japan and Argentina to also advance. Canada and the U.S. finished with seven points but the Canadians took top spot in the group by virtue of beating the Americans.
The win over the U.S. was sweet for the Canadians, who had lost their three previous meetings with the Americans this season. The U.S. came into Glasgow ranked sixth in the standings while Canada was 11th.
That means Canada and the U.S. will likely face off in a regional Olympic qualifier in June.
Mike Fuailefua, Ciaran Hearn, Conor Trainor, Sean White, Adam Zaruba and Liam Underwood scored tries against the Americans while Harry Jones kicked five conversions.
Captain John Moonlight and White scored against Argentina with Jones adding a conversion.
Moonlight opened the Japan game with a bruising try, running over several smaller Japanese players. Sean Trainor and Sean Duke scored two tries while Underwood added a single for Canada. Jones kicked four conversions.
It could have been more but Zaruba, on a breakaway, dropped the ball before getting to the goal-line. Canada's Pat Kay was sent to the sin-bin in the dying seconds.
The Canadians made history in Glasgow last year when they made a Series final for the first time. They lost to New Zealand 54-7 in the championship game.