Hatton, who had equalled the Old Course recod with a 61 on Saturday, birdied the 18th to card a closing 70 and finish 24 under par, one shot ahead of Belgium's Nicolas Colsaerts.
The Englishman, who joined the breakaway LIV Golf tour earlier this year, also finished second in the pro-am event alongside his father.
"It's the first time I've actually won the tournament with my dad here so it means a lot," said Hatton.
"To do it at the home of golf is really special. I'm trying not to cry to be honest. I'm a bit lost for words."
Birdies on the second, fifth, 10th and 11th had given Hatton a comfortable three-shot lead with six holes to play, only for the Ryder Cup star to run up a double bogey on the 13th and drop another shot on the next.
But his birdie at the last was enough for victory after Colsaerts missed from eight foot on the 18th with the chance to move to 24 under.
Tommy Fleetwood was third on 21 under.
Denmark's Thorbjorn Olesen and Irish businessman Dermot Desmond, the majority shareholder of Celtic, won the team event on 48 under par.
