"When I was standing on the first tee, I looked at that wall (of champions) and in my head I engraved my name on it," Na told reporters after the victory, his third on the PGA Tour.
His winning score of 13-under 267 included a near-course record 62 on Friday as he joined Ben Hogan, Sam Snead, Arnold Palmer, Jack Nicklaus and Lee Trevino as winners at Colonial.
"I knew before my career was over I was definitely going to win out here, if not multiple times," Na said.
"It's nice to get one, and who knows, maybe I'll win a couple more times before my career is over here."
Finau (68) needed a birdie at the last to finish at nine-under with Andrew Putnam (66) and Taiwan's Pan Cheng-tsung (69) tied for third at eight-under.
Jonas Blixt rebounded from a disappointing third round to take fifth on seven-under as the Swede shot 68.
Hometown favourite Jordan Spieth went in the opposite direction as his putting deserted him, leading to a two-over 72 that left him eight strokes behind Na.
The former champion missed a 12-footer for birdie at the first hole and then bogeyed the second as his tee shot went into a fairway bunker.
He did not make a birdie until the last hole.
"I just misread a number of putts today just by half a cup," said Spieth, who was off target on the lengthy putts he had made in the first three rounds.
Defending champion Justin Rose finished at five-over with a 70.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Greg Stutchbury)
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