Cooke, together with Italy's Guderzo, Johansson of Sweden, Christiane Soeder of Austria and Denmark's Linda Melanie Villumsen Serup, led the field going into the final 10km.
At the bottom of the final climb, Cooke seemed to drop away from the other four riders as they turned the wet and slippy corner.
But she put on the gas during the lung-bursting slope to the line and had enough in the tank to edge home first.
"All congratulations to Nicole for a fantastic victory," said Olympics minister Tessa Jowell.
"What you can't perhaps quite sense at home is just the torrential rain that was falling on Beijing - and despite those incredibly tough weather conditions, she won. So it's a wonderful victory and a huge lift for Team GB."
And Sports Minister Gerry Sutcliffe added: "This is a great start to the Beijing Olympics for Team GB and I have no doubt this medal will fire up the rest of the team to do their best in the next two weeks.
"Well done to Nicole Cooke - she has set us on our way."
Marianne Vos of the Netherlands, a former world road race champion, ended up in sixth - 21 seconds behind - together with Athens silver medallist Judith Arndt of Germany.
"Normally I'm good in the rain, but the problem was that it was really cold," said Vos, who was one of the pre-race favourites. "We expected warm weather."
French great Jeannie Longo, 49, competing in her seventh Olympics, finished 33 seconds behind the winner in 24th.
Cannot play media. Sorry, this media is not available in your territory.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.