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The 34-year-old holed eight birdies and an eagle to finish on 11 under, with Italy's Francesco Molinari moving up to second after a four-under 68.
Sweden's Henrik Stenson (68), Belgium's Nicolas Colsaerts (65) and Japan's Hideto Tanihara (68) were two back.
England's Graeme Storm (68) was the top home nations player on seven under.
He was joined by Ireland's Shane Lowry and Australia's Andrew Dodt, who jointly led overnight with Branden Grace but finished with a one-over 73.
South African Grace trailed Noren by two shots with seven holes remaining but his challenge effectively ended with a double bogey on the 11th after he failed to hack his ball out of a ditch and was then forced to take a penalty drop.
World number 13 Noren, who began 10 pairings ahead of the final group, told Sky Sports: "It feels amazing. I've been in the players' lounge for the last two hours. I was so nervous. It finally went my way."
He was seven shots off the lead following a double-bogey on the last hole on Saturday, but made it to the turn in 31 and picked up further birdies on the 12th, 13th, 14th and 16th.
Noren then capped off a brilliant display with an eagle at the last after his five-iron approach from 204 yards finished just four feet from the pin.
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"I've been envious of the champions of the past," added the Swede, who won £894,000.
"I looked at the score a lot at the 12th and 13th holes - I didn't have a clue what I was going to shoot."
England's Lee Westwood, who began the day three off the lead in the penultimate group out on the course, carded a final round one-over 73 to finish joint 14th.
Sweden's Alexander Noren produced a stunning 10-under-par 62 to break the Wentworth West Course record and win the PGA Championship by two shots.