Earlier, England knocked South Africa out of the Cup competition, winning their quarter-final encounter 17-12 as Dan Norton scored in the dying seconds of the match to bring the home side a win in front of their fans.
South Africa secured the world series title last weekend as they won the cup final in Paris. Trailing 21-0 at half-time it seemed like that sorry statistic had the shelf life of atomic waste. Scotland's Mark Robertson was named player of the final.
Australia did not win a tournament in a 2016-17 season beset by injuries and the loss of players to the 15-man game, including star Cam Clark (NSW Waratahs).
The Americans added a consolation try with no time remaining.
In the two victories, the Aussies scored a combined 85 points with just one unconverted try posted against it.
Their hopes of breaking that drought disappeared in the quarter-finals when they lost 24-21 to eventual tournament champions Scotland, having squandered a 21-0 lead following tries to Sam Dickson, Fa'asiu Fuatai and Andrew Knewstubb.
England had the upper hand in the first half of the final after a superb solo try by winger Dan Norton, who recently became the highest try scorer in rugby sevens history.More news: Rolf Harris released from Stafford Prison
Then in a surge up the middle of the field, full of support play, Scotland captain Scott Riddell was on hand to finish off, and they held on to give departing coach Calum MacRae and retiring players Mark Robertson and Scott Wight a flawless send-off.
The Canadians finished 13th, ninth and sixth, respectively, over the last three seasons on the World Series.
"It says an very bad lot about the consistency of this group and the way they keep fighting hard day in and day out for each other and their determination to make England proud".
"Beating New Zealand in the manner that we did and our second-half performance in the final were extremely pleasing".
"If you're a hard team to beat you're always going to have an opportunity to win, especially with the firepower we have in attack".
LONDON -Canada capped off a stirring World Series season with a bronze medal Sunday at the London Sevens. At least this squad went out at the top after a memorable victory in West London.