Azalea shares her name with the par-five 13th hole at Augusta National where her father last year sunk a seven-foot putt in the final round to save par after landing in the bushes and taking a penalty drop.
Garcia, who will defend his title next month, was trailing Justin Rose by two strokes at the time and a slip-up would have probably handed the Englishman victory.
Garcia went on to force a playoff in which he beat Rose on the first hole to end nearly two decades of major heartbreak.
"So proud and impressed with my wife @TheAngelaAkins and the way she handled the pregnancy and delivery! Love you both so much," he added.
(Reporting by Aditi Prakash in Bengaluru, editing by Ed Osmond)
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