The Canadian men finished tied for seventh, beaten 14-7 by England in a Cup quarter-final earlier in the day.
Sean Duke and Pat Kay scored tries for Canada against Scotland, with Harry Jones adding a conversion.
A late Scotland try by Fijian-born Joseva Nayacavou proved to be the difference.
Later Sunday, Fiji beat defending champion New Zealand 24-17 in the Cup final and took over first place in the overall standings.
The Fijians can win the nine-event HSBC World Series title for the first time in nine years next weekend by reaching the final of the London Sevens, the series closer.
"We've got ourselves in a terrific position," Fiji coach Ben Ryan said. "Third place (in London) could do it for us, but we want to back-to-backs."
South Africa and New Zealand were second and third in the overall standings, and the three top teams have all booked their tickets to the 2016 Olympics, which will mark the debut of rugby sevens.
The top four in the table at the end of the season qualify automatically for the Rio Games. England finished third in Glasgow and was fourth overall after Sunday's play, 16 points up on Australia.
Canada remained 11th.
Jones' converted try gave Canada an early 7-0 lead against England in the Cup quarter-final, but tries either side of halftime gave the English the victory.
It marked the second straight tournament that the Canadians have reached the Cup quarter-finals. They finished fourth last time out in Tokyo.
The Canadians made history in Glasgow last year when they made a HSBC World Series final for the first time. They lost to New Zealand 54-7 in the championship game.
Canada went 2-1-0 Saturday in winning its group, defeating the U.S. and Japan and losing to Argentina.
South Africa ended up fifth in Glasgow as the plate winner and fell five points behid Fiji. New Zealand, the four-time defending series champ, was eight points behind the leaders heading to Twickenham.
Fiji enjoyed some luck in the final. Savenaca Rawaca scored the first try but New Zealand should have finished the first half out of sight.
Sam Vaka was denied a try for an alleged double movement, and robbed of a second when he was tackled around the neck by Fiji captain Osea Kolinisau, and received only a penalty.
The pressure finally told when tries by Sherwin Stowers and Sam Dickson put New Zealand 12-5 up at the break.
"We were awful," Ryan said. "New Zealand only had nine players (because of injuries), so we had no excuse to put them to the sword."
Following the halftime roasting from Ryan, Fiji scored 70 seconds into the new half through Kolinisau, but at the expense of playmaker Pio Tuwai.
His injury replacement, Apisai Domolailai, finished the next two tries, the second while New Zealand's Scott Curry was in the sin-bin, to make it 24-12.
Curry scored from his own chip ahead to give the Kiwis a chance in the last minute, but Fiji turned over ruck ball in front of its line to secure its fourth title from eight tournaments.
New Zealand was consoled by securing a berth in the Olympics when Australia lost its quarterfinal. Australia lost even further ground in the race for the fourth available Olympic spot to England, which finished third in Glasgow and can virtually buy its ticket to Rio.
— With files from The Associated Press