Johnson, who began the tournament with a first-round 65, carded a four-under 68 to finish five shots clear of Australia Cameron Smith and South Korea's Sungjae Im in second.
Smith became the first player to ever shoot all four rounds in the 60s. In 84 stagings of the Masters, Smith and Im's scores of 15-under would have been enough to earn a green jacket in 79 of them.
Im broke the record for the lowest total score on Masters debut.
Justin Thomas finished in fourth at 12-under with South Africa's Dylan Frittelli and Rory McIlroy of Northern Ireland a shot back in fifth.