McIlroy started the day tied for sixth at 5-under and four strokes behind the leaders but his 1-under round allowed him to improve four spots to a four-way tie for second.
The Northern Irishman eagled the 14th at Carnoustie to move into a share of the lead but he finished two shots behind victor Francesco Molinari.
Birdies at the ninth and 11th restored his hopes before he celebrated wildly after sinking a 50-foot putt for an eagle three at the 14th.
"Sunday at Augusta was a big learning curve again for me because, even if I hadn't won that tournament but I went down swinging and aggressive and committing to every shot, I would have walked away a lot happier", he said.
"I have no regrets". I played the way I wanted to play this week.
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"Today I did everything I thought I needed to do to win the championship", he said, adding that he expected a consolation phone call from tennis champion Serena Williams, who lost the Wimbledon final eight days ago.
Two hours earlier, Woods had one hand on the Claret Jug for what would have been the fourth time after surging to the lead with a flawless front nine on a day when the previously missing wind finally bared some teeth. The group of 39 includes a Xander (Schauffele) and a Zander (Lombard), the latter a 23-year-old South African with one previous major participation in his life, yet who briefly held a share of the lead in the second round before two bogeys, and said: "Yeah, it was pretty cool". It gives me a lot of encouragement going into the final major of the year.
"When I made the eagle on 14, it was tough to get close on 15, 16, and 17".
"I'm lost for words really", said Molinari.
"But I think anything under par out there today was a good score". I just sort of ran out of holes at the end. This is the same player who, after a particularly soggy British Open round at Royal St. George's in 2011, said he was "not a fan of golf tournaments that the outcome is predicted so much by the weather".
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