He has a two-shot lead over Finau and Woods, who is certain to be cheered on by a massive gallery as he looks to end an 11-year major title drought by claiming a fifth Green Jacket.
National Basketball Association stars LeBron James and Steph Curry also expressed their admiration, although Curry hoped for a little more from Woods as a result of him claiming a fifth green jacket.
But it was the 43-year-old's first Masters title since 2005.
"I'm pretty comfortable being in, being up there on the leaderboard in a major come Sunday", said Koepka, whose roller-coaster round included an eagle, five birdies and four bogeys. "When I tapped the putt in, I don't know what I did but I know I screamed".
It's the first time Woods has won a major when he didn't hold the 54-hole lead, and sets a new record for the longest gap between Masters victories.
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It called on protesters to maintain a sit-in outside the defense ministry that started on Saturday, a source with the group said . They vowed to continue the protest even though a curfew has been imposed as part of the three-month state of emergency.
Woods, Molinari, Xander Schauffele, Brooks Kopeka and Dustin Johnson with Australian Jason Day in the clubhouse on 11-under and Patrick Cantlay, who also hit 12-under, foiled by bogeys at 16 and 17.
Professionally, it's an impressive comeback for sure after Woods' was forced to undergo surgeries for back and leg injuries that almost ended his career. "My dad was here in 1997 and now I'm the dad with two kids there".
All those moments built to Sunday, when Woods was once again his old familiar dominating self.
On a day when Augusta National, which had been softened by rain earlier in the week, was yielding low scores Koepka could only muster a three-under-par 69 that left him alone in fourth place and three shots back of leader Francesco Molinari.
Paired together in the final round of last year's British Open, won by the Italian at Carnoustie, Molinari and Woods found themselves in the last group again battling for a major title. "I'm so happy for him and for the game of golf this is so fantastic". 79-year-old Nicklaus posted on Twitter.