Glover and Stanning won Britain's first gold of the London 2012 Games last summer with victory in the women's pair, but the latter has since taken a break from rowing with Swann coming in as the 27-year-old's new partner.
The new pair came into the World Championships unbeaten and were victorious over the Romanian partnership of Roxana Cogianu and Nicoleta Albu by more than eight seconds after crossing home in 7:17.73minutes.
That was one of three podium finishes on the penultimate day in South Korea with Graeme Thomas, Sam Townsend, Charles Cousins and Peter Lambert taking Britain's maiden men's quad world medal.
They came from the pack to take bronze behind Croatia and Germany while Peter and Richard Chambers claimed the third medal of the day with third in the lightweight men's double scull.
That adds to the bronze medals Britain won lightweight men's pair and women's single the day before with Glover revealing how the situation she now finds herself in makes this world gold different to her Olympic title.
"It has been a very different year. Last year Heather and I were pretty much unknowns outside rowing but this year there has been pressure of expectation on Polly and me. I think we handled it pretty well," said Glover.
"It was very different this year because even though last year was the home Olympic Games I actually had less pressure, we were relative unknowns and kept away from the media. This time we had to deal with the pressure of expectation and I think we did it well.
"Sometimes you think it will take a long time to get such a good connection with a rowing partner as I had with Heather but Polly and I have worked really hard and it has come together well."
Elsewhere Imogen Walsh and Kathryn Twyman were fourth in the lightweight women's double scull and Alan Sinclair, Nathaniel Reilly O'Donnell, Scott Durant and Mat Tarrant were fifth in the men's four.
And GB Rowing performance director Sir David Tanner took great satisfaction from all five of those performances in South Korea, not just the three crews that worked their way onto the podium.
"We have had three really good medals and two other strong A final performances," he said. "There is history with Polly Swann taking a debut gold and Helen Glover, the Olympic champion, adding a world title to her Olympic gold.
"The Chambers brothers have swapped from sweep rowing to the double scull this year. That was the challenge for them and to be on the podium a year after their Olympic silver in the lightweight men's four in a completely different discipline is exceptional.
"And, with the men's quadruple scull, that's a breakthrough moment for the GB Rowing Team. A piece of rowing history. We have never done that before. I am really happy with our three medals."
© Sportsbeat 2013