The USA took an early lead through Marcus Fasitupe Tupuola before England got on the board through Dan Norton.
Will Edwards helped England to a 14-7 lead at the break, and further tries from Harry Glover and Mike Ellery sealed victory.
England had earlier beaten Australia 31-19 in the quarter-finals, but lost their semi-final 26-12 to Fiji.
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“The growth that some of our young guys have shown is really encouraging,” head of England Sevens Simon Amor said.
“There have been some frustrating performances across the last couple of weeks but its obviously pleasing to be back on the podium.”
In the battle for fifth Australia fought hard against New Zealand, with neither team unable to break the deadlock of 22-22 in 14 minutes. The match went to golden point extra time with the All Black Sevens finding the try line to advance to fifth place final.
Qantas Australian Mens Sevens Head Coach, Tim Walsh said: The tournament was an improvement and there were some positive signs for the team and individuals.
There is no such thing as luck – you earn opportunities and we are learning to play smarter and harder.”