Starting third from last after a fine qualifying session, Clarke beat Peter Kauzer's time by 0.17 seconds to grab first place with two paddlers left to go.
Czech star Kiri Prskavec was first up and was far quicker down the course, but picked up a two-second penalty.
That left only fastest qualifying Jakub Grigar who could beat him - and the Slovakian made a mistake which cost him time in the final stretch, missing out on the medals and leaving Clarke as the champion.
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Kauzer ended up with silver and Prskavec bronze.
"Everything pieced together so nicely, I can't put it into words. I knew I was capable but to put down that run in the Olympic final, it is a dream come true," Clarke told the BBC.
"It is hard to put it into words how much work has gone into this. I have spent a lot of time here, I know this course like the back of my hand and it has paid off.
"There has been lots of ups and downs but it is just fantastic."
Clarke hadn't been in the frame for a medal at all before the Games began, having enjoyed solid but unspectacular results over the past few years.
But he produced two of the runs of his life in Rio, balancing aggression and safety perfectly to end up as Britain's second Olympic champion of the Games.
"When I woke up I struggled to have breakfast I was so nervous with all the emotions," he added.
"I thought if it goes to plan I could come away with a medal but to be Olympic champion it is something you dream about."
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