This is the first time that the Blitzboks exit at the quarter-final stage of the World Rugby Sevens Series since May a year ago, when they lost to Samoa at the Paris Sevens.
The Cup win came in Canada's 140th event on the circuit.
The second half began with American speedster Baker scoring his 41st try of the season as United States drew level with Canada 19-19.
"No one worries about you that much, and after our (pool stage) loss to Fiji, the big teams probably weren't anxious about us too much today", he said.
They scored two tries, through Tom Lucas and then Anderson in the final act of play with Dylan Sage sin-binned for a deliberate knock-down, which proved to be the clincher. But we showed up today, we showed the world we can beat anyone.
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Coach Damian McGrath said: "The game plan was to go in, hold the ball and put them under pressure - and we did just that".
Sione Molia bagged a double in the 36-14 romp against Wales before it was Ware's turn to secure a brace in their 21-14 defeat of the risky U.S. side.
The men's team took down two top-notch contenders, New Zealand and England, before beating the US 26-19 to claim the final. The other three have resulted in semi-final exits.
Looking at the Paris 7s next month, Fiji will face Russia, Samoa and Australia in Pool D.
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