The 51-year-old Japanese, a relative unknown on the Champions Tour circuit, sank a long birdie putt on the 17th en route to a sterling round of 6-under-par 65 at Bellerive Country Club.
He ended at 11-under-par 273, two strokes ahead of the field in notching his first-ever major championship.
Third-round leader Kenny Perry (72) was ahead by as many as three strokes Sunday but fell short in his bid for a third career title after carding a double-bogey on No. 5 and then stumbling to two more late bogeys.
He was joined in second place by Jay Haas (70) at 9-under 275.
Sole possession of fourth at minus-8 went to Mark O'Meara (65) while Kiyoshi Murota (67) took fifth at 7-under.