Heath, 32, claimed victory in 35.197 seconds, just 0.165 seconds faster than silver medallist Beaumont.
Spain's Saul Craviotto and Germany's Ronald Rauhe tied for bronze, with identical finishing times down to the thousandth of a second.
Heath said he was overjoyed by the results.
"I could be up with Jesus Christ looking down," said Heath. "It's an absolutely incredible feeling. Hard to put into words."
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The British paddler won silver in the men's K-2 200m race on Thursday. In the 2012 Games, he took bronze in that same event.
(Editing by Nina Chestney)
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