The victory secures Canada's place the 15-country world series tournaments for the 2012-13 season.
"We set out a goal and we wanted to win the tournament and knowing that if we won, we got core status," stated Canada coach Geraint John. "So we've achieved two goals this weekend. Credit to the players, they worked really hard this year."
In the tournament's title match, Waisea Nayacalevu's second try of the match with two minutes left gave Fiji a 35-28 win over defending champion New Zealand.
Canada, meanwhile, finished atop its Pool group after sweeping the third day of the tournament, including a 24-7 quarter-final victory against Russia and a 14-12 win over Portugal in the semifinal.
"We knew what we had to do and we knew what the status was in terms of how to become a core team," said John.
"We decided that one thing we weren't going to talk about was the word core. All we said was we were going to try to win a tournament. That was the big emphasis all weekend. That was a deliberate thing we did."
Duke scored two tries and Conor Trainor one in the win against Russia, while captain Nathan Hirayama's goal kicking was the difference against Portugal.
In the final, Canada was able to relax knowing they had already secured core team status.
By becoming a core team, Canada will now compete at every IRB world series tournament. It also mean that Canada is better prepared when rugby sevens is introduced into the Olympics in 2016.
Spain and Portugal also earned status as core teams.
Fiji's win moved it to within two points of leader New Zealand in the overall IRB sevens world series after six of nine tournaments. The New Zealanders have 111 points, Fiji 109 and third-place South Africa, which came third in Hong Kong, 93.
Branco du Preez scored a try and kicked four conversions for 13 points in South Africa's 28-0 win over England in the third-place match.
Earlier, Jack Wilson and Lolagi Visinia scored early first-half tries to lead New Zealand to a 19-12 win over South Africa in the semifinals, while Fiji beat England 14-7.
In the quarter-finals, England scored a late try to beat Australia 19-14 and Fiji defeated Argentina 26-7, while South Africa ended Samoa's unbeaten run with a 27-14 win and New Zealand defeated Wales 31-7.
- with files from The Associated Press.