The 24-year-old from High Wycombe is chasing his first European Tour victory and a £640,380 winner's cheque.
Hatton's nearest challenger is compatriot Ross Fisher who is three shots back on 14 under par.
"This round is clearly the best round I've ever had," he said.
"I've never actually got to double digits under par before, so I'm very pleased with that.
"The goal now is to get a win. But then it's been a really consistent year, and it would be nice to have a good finish."
Hatton's 10-under 62 at the Old Course - his lowest score on the European Tour - is matched by six other players, including fellow Britons Paul Casey and Tommy Fleetwood.
Sweden's Joakim Lagergren and South Africa's Richard Sterne are four strokes behind on 13 under.
Danny Willett and Lee Westwood - part of Europe's defeated Ryder Cup team in Hazeltine last weekend - are well off the pace on six and 10 over respectively.
However Spaniard Rafael Cabrera-Bello, who took two and a half points from his three matches against the Americans, is better placed on eight under.
England's Tyrrell Hatton will take a three-shot lead into the final round of the Dunhill Links Championship after he equalled the St Andrews Old Course record with a 10-under-par 62.