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Archibald, Laura Trott, Joanna Rowsell-Shand and Elinor Barker set a new world record of four minutes 10.236 seconds, comfortably ahead of the United States.
"We were convinced it was going to go down to the wire," said Archibald, 22.
"America come out harder than us. In all the previous rides we've not been up until the last kilo."
The Americans finished in four minutes 12.454 seconds, unable to match the intensity of the British women.
Archibald, from Milngavie, near Glasgow, said in the immediate aftermath: "I had a sneaky look at the end to see if we were there and once you get that champing-on-the-bit sensation, we felt like super heroes, I suppose.
"It's pretty special. I've not won a team pursuit since the Europeans this year.
"It's all the cliches at the moment; it's overwhelming, it's a dream come true, because nobody really expects that they'll make that gold medal.
"Every athlete goes through their injuries and trials and tribulations and whatnot. It will kick in in about 10 minutes, no doubt, and the legs will start hurting."
Archibald's achievements are all the more remarkable given she ruptured her posterior cruciate knee ligament and fractured her elbow in a motorbike crash last December, causing her to sit out the World Championships in March.
Her gold medal for Team GB has helped make the Rio Games Scotland's most successful Olympics on foreign soil with 10 medals won so far, surpassing the eight from Sydney 2000, and two more - for tennis star Andy Murray and cyclist Callum Skinner - to follow on Sunday.
"That feels pretty special, pretty exciting for the Gold Coast in 2018," Archibald said, with an eye on the next Commonwealth Games, where Scotland compete as a separate nation.
"It's pretty mad, with Callum [Skinner, also a gold medal winner] getting in the track cycling scene, that progression over the last few years.
"I train as GB most of the year until the Commonwealth Games so it's exciting when you see people that you've seen for years go through different programmes and different levels and now we're all at the top."
Katie Archibald admitted to being surprised at the margin of victory as she helped Great Britain win Olympic gold in the women's team pursuit.