Taking a five-shot lead into the final round, Hatton recovered from finding the Swilcan Burn with his approach into the first to chip in and save par.
The victory is Hatton's second on the European Tour and he now becomes one of four men to successfully defend a trophy for their first two wins.
"Obviously I'm very happy", added Hatton, who took a share of the previous course record of 62 when winning the tournament a year ago.
Just imagine the damage someone like Dustin Johnson could have done on a day like Sunday round there, though McIlroy, admittedly, is another of the game's long-hitters and that didn't seem to do him any good on this occasion.
Hatton didn't feel Fisher's galloping footsteps behind him until he was nearly home, and it stiffened his resolve for the final two holes.
"It was very special because it was at the end of my season, and I played amazingly like the rest of the week but today it feels like all the putts went in", he said. "We've just had good fun, I think that is what this tournament is about". "So I played the next 44 holes in 15-under which is pretty satisfying", added the 2016 Joburg Open who won this year's Czech Masters in Prague to seal his second European Tour title.
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The two sides faced each other earlier this year in Dortmund, with Germany coming out on top with a 1-0 win . He added: "It's hard playing under pressure, but when it's added pressure like that, it doesn't help".
One pairing ahead of him, Ross Fisher was producing one of the greatest rounds ever seen on the Old Course. "I got off to a fast start and managed to make some good putts early on".
It was also a three shot lead for the winning team of Kieran Mcmanus & Jamie Donaldson, who shot 40-under-par through the 4 days of competition.
"Unfortunately I've got to sign for a 61 but I'll definitely take it".
Nine-time major victor Gary Player tweeted that he was "delighted for all the players" on their scoring but also said "it's quite sad to see The Old Course of St Andrews brought to her knees by today's ball and equipment".
Playing his first event since becoming a father for the first time last week, Fleetwood birdied six of the last eight holes to complete a bogey-free round and beat the course record by a shot. "I didn't hit a lot of quality shots off the tee coming in like I needed to".
Another man who also made significant strides up the season rankings is Robert Rock.