Northern Ireland's McIlroy shot 1-over-par 73 to be tied with England's Justin Rose, who posted 66 and waited for McIlroy to finish. They both shot 11-under, 277, for the week.
Re-playing the 18th hole at Augusta National Golf Club, McIlroy's approach shot rolled back toward the hole and inside Rose's ball. After Rose missed a birdie attempt and notched a par, McIlroy didn't flub another chance for a victory.
McIlroy needed par at No18 to win in regulation, but after blasting from a greenside bunker on the 18th hole he rolled a 5-foot par putt too far to the left.
The new champion recovered from a near-disastrous stretch on the back nine to birdie the 17th hole for a brief one-stroke lead. McIlroy's bogey on No11, double bogey on No13 and bogey on No14 appeared to send him on track for another final-round collapse at a major.
But instead, McIlroy recovered for a birdie on the par-5 15th hole then stuck his approach on No17 and sank the putt to take the lead.
It marked the fifth major championship for McIlroy, and his first since capturing the PGA Championship for the second time in 2014.
Patrick Reed (69 on Sunday) was third at 9 under. Defending champion Scottie Scheffler (69) placed fourth at 8 under, giving him four consecutive top-10 finishes at the Masters.
Rose was the leader after the first and second rounds, and after a tough 75 on Saturday he made a major final-round push. He had only four pars on his card -- countering four bogeys with 10 birdies.
Bryson DeChambeau, who figured to be McIlroy's biggest threat and in the final pairing, took the lead after the second hole before stalling with back-to-back bogeys and a string of pars to skid off the path. By the time he double-bogeyed No11, he was tied for ninth and seventh strokes back.
DeChambeau's 75 left him at 7 under, tied for fifth place with South Korea's Sungjae Im (69).
