Thomas vaulted to the front with four birdies in a sizzling seven-hole stretch mid-round and held firm over the dangerous final water-lined three holes, known as the 'Green Mile.'
The 24-year-old from Kentucky made a rare birdie at the par-three 17th to all but secure victory and a bogey at the last was academic as he carded 68 to finish at eight-under 276.
Fellow American Patrick Reed (67) bogeyed the last to finish equal second with Italian Francesco Molinari (67) and South African Louis Oosthuizen (70).
Hideki Matsuyama, seeking to become the first man from Japan to win a major, held the lead briefly mid-round before fading with three consecutive bogeys from the 11th.
He carded 72 and finished three shots behind with American Rickie Fowler (67).
Overnight leader Kevin Kisner (74) finished four shots back.
Thomas, one of the longest drivers on tour, came into the final major of the year ranked 14th in the world, though not one of the favourites after recent poor form.
But he came through by executing under pressure as some of his rivals withered, joining his good friend Jordan Spieth, with whom he shared a house at the British Open last month, in the major champions club of 2017.
Thomas also joins Spaniard Sergio Garcia (Masters), American Brooks Koepka (US Open) and Spieth (British Open) as the year's major champions.
