Former European silver medallist Stamper from Liverpool claimed the featherweight (-68kg) title.
And 17-year-old Jones turned the previous day's -57kg bronze into a lightweight (-62kg) gold.
It took the 10-strong squad's final medal haul to six.
Dad of one Stamper, 24 and six times National champion, defeated Mexican rival, Idulio Isklas Gomez to seal a memorable win.
Reflecting on his victory he said: "It was an amazing day and one of my best ever in the sport.
"I had great support from the staff and players to get me through six tough fights.
"Hopefully this is the start of big things to come in the run up to [London] 2012."
Teammate and roommate Tony Grisman lost in the quarter-finals of the same weight class to Brazilian bronze medallist Diogo Silva.
Jones, from Flint, shrugged off any tiredness from her earlier exertions by beating American Paige McPherson on a golden point in her final.
It took her total number of fights to eight in two days.
After claiming her first senior title, she said: "The main focus for me was to get experience on the LaJust scoring system for the World Championships in May.
"I didn't expect to fight at two weights so I am really happy with two medals.
"It was a tough tournament with lots of high quality fights.
"Now I'm looking to do the same in the German Open in two weeks time."
The British team won·further bronze medals from Aaron Cook in the -80kg, Damon Sansum in -87kg and Sophie Dickson -55kg junior division.
GB Performance Director Gary Hall said: "This has been a fantastic weekend for British Taekwondo and a real boost to our preparations for the World Championships in a couple of months time.
"We have had some excellent performances distributed right across the team.
"It's been great to see experienced performers, such as Martin Stamper and Aaron Cook, achieving medal success.
"At the same time it was fantastic watching new young players such as Damon [Sansum], Sophie [Dickson] and indeed Jade continue to make a mark on the world stage.
"We've still got a lot of hard work to do in the coming weeks but this will give us confidence as we prepare for [the World Championships] Korea."