Tour de France winner Wiggins dominated the 44km ride to beat Germany's Tony Martin by 42 seconds, with Britain's Chris Froome taking the bronze.
Wiggins moves one medal clear of former rower Sir Steve Redgrave as the most successful British Olympian of all time.
"It was phenomenal, the noise was amazing," said Wiggins, who pretended to conduct the national anthem after receiving the fourth gold medal of his career outside Hampton Court Palace.
"It will never, never get better than that. Incredible. It had to be gold today or nothing. What's the point of seven medals if they're not the right colour? Mainly it's about the four golds. Now I have to go to Rio and go for five."
Best of British
- four gold, one silver, two bronze
Sir Steve Redgrave
- five gold, one bronze
Sir Chris Hoy
- four gold, one silver
- three gold, two silver
- three gold, two bronze
Sir Matthew Pinsent
- four gold
- four gold
- three gold, one silver
Chris Boardman, who won Olympic cycling gold in Barcelona at the 1992 Olympics, described Wiggins's performance as "untouchable".
"His sporting performances this year have been unprecedented. The greatest British cyclist of all time, I have no qualms about saying that. One of the top British sportsmen, also."
Glover and Stanning led from start to finish to become the first British female rowers to win an Olympic gold.
Stanning, who has taken time out from her army career to compete in the Olympics, said: "I want to collapse I'm so overjoyed. We hope this is the start of things to come from the Great Britain team."
PE teacher Glover added: "I really hope my story can be an inspiration for kids in PE watching this, or at home thinking about taking up a new sport. Just go on, go for it, you don't know what's going to happen."
Prime Minister David Cameron said: "I'm delighted about Heather and Helen's gold medal in the rowing - an absolutely fantastic effort."
Mr Cameron, on a visit to the Giant's Causeway in Northern Ireland, added: "I was sitting in the wishing chair, I was told I could make my wish. I won't say what it was, but as soon as I got back to my mobile phone I had the good news. Fantastic news, well done to them, a great success for the United Kingdom team."
Mayor of London Boris Johnson said Glover and Stanning's triumph would be celebrated throughout the country.
"Not only have they achieved the first gold medal for Great Britain at London's Games, they have bagged the first-ever rowing medal for Team GB's women at an Olympic Games," he said.
GB get bronze as Germany win men's eight
"It is an outstanding achievement and I am sure it will spur on all our athletes in the medal stakes. It is fantastic - go Team GB."
Royal Mail announced that images of Wiggins and rowing duo Glover and Stanning would appear on special sets of stamps, which would be available in 500 Post Office branches on Thursday.
Forty minutes after the women's pair success, Great Britain's men's eight claimed bronze as world champions Germany took gold in a thrilling final.
The crew, featuring 1992 gold medallist Greg Searle, pulled ahead of Germany at halfway, but ran out steam with Canada pipping them on the line for silver.
Team GB could taste more glory in the Aquatic Centre when Michael Jamieson and Andrew Willis compete in the men's 200m breaststroke final after qualifying first and third from the semi-final.
There was disappointment for Britain in the
women's time trial
as Beijing silver-medallist Emma Pooley finished sixth and Lizzie Armistead, who took road race silver on Sunday, came 10th.
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