Stanning and partner Helen Glover rowed to a glorious gold medal in the women's pair before cyclist Bradley Wiggins triumphed in the men's time trial to become Britain's most decorated Olympian.
Scots swimming sensation Michael Jamieson came within millimetres of making it a historic hat-trick but had to settle for silver after being edged out by Hungary's Daniel Gyurta.
Britain also picked up two bronze medals yesterday through Chris Froome in the men's cycling time trial, won by Wiggins, and the rowing men's eight.
Stanning, from Lossiemouth, and Glover became the first British female rowers to win an Olympic gold when they destroyed the field at Eton Dorney.
After being presented with her medal, Stanning, a former pupil of Gordonstoun School in Moray, where Zara Phillips – who won silver in equestrian team eventing on Tuesday – also studied, said: "I'm so overjoyed."
The 27-year-old Royal Artillery officer, who is expecting to be deployed to Afghanistan next year, added: "I want to collapse. I'm probably talking rubbish now.
"We got out ahead throughout the season and we wanted to do that today, and not give anything back. Helen was telling me to keep on going."
Army colleagues at Camp Bastion, in Afghanistan, cheered as Stanning and Glover crossed the finish line. Stanning said: "I am really proud of being part of the forces, and the Army has been fantastic to get me to where I am. Thanks for all the support in Afghanistan, I'm so proud to be associated with you."
Stanning's commanding officer, Lieutenant Colonel Craig Palmer, said: "We are delighted with Heather's win. Soldiers from 32nd Regiment Royal Artillery were thrilled to watch the race from their bases in Afghanistan, while their friends and families watched it here in the UK.
"I am sure they have been inspired by her performance."
The British duo led their final from the start and were roared home by thousands of ecstatic fans at Eton Dorney and millions more watching at home.
After crossing the finish line Stanning collapsed backwards into Glover's lap before they saluted a delirious crowd, which included Princes William and Harry and the Princess Royal.
Just a few hours later Wiggins completed a historic double of the Tour de France title and Olympic gold within the space of two weeks. The 32-year-old also became the most decorated British Olympian, with four golds, one silver and two bronze medals, overtaking Sir Steve Redgrave's tally of six medals – five gold and a bronze.
After the race, Wiggins said: "It was phenomenal, the noise was amazing. I don't think my sporting career will ever top this now. That's it. It will never, never get better than that. Incredible. It had to be gold today or nothing."
Jamieson, who came to London as far more of a medal outsider, said: "I was desperate to get on the podium tonight to repay the faith and support we've had.
"I couldn't have done any more. It was everything I hoped it would be – the crowd bringing me down the final 50 metres was the greatest experience of my life."
Prime Minister David Cameron described the successes in rowing and cycling as a "golden moment for Britain".
He added: "This is really going to put rocket boosters on it for the whole country. I'm very, very excited."
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