Fleetwood, leader in the Race to Dubai standings, shot a blemish-free 9-under-par round at the venue for next year's Open to join Hatton on 11 under.
Hatton, who was also playing his second round in the three-course event at Carnoustie, did not drop a shot either in a 7-under-par 65.
The pair led by one shot from Belgium's Nicolas Colsaerts, who shot 67 at St Andrews after recovering from a double bogey on his first hole.
World No. 6 Rory McIlroy, hoping to end a frustrating year with a win, was overshadowed by Fleetwood, who was one of his playing partners.
McIlroy ended the day 11 shots off the lead on level par after a 71 which included a double-bogey seven on the sixth hole. With the cut coming after 54 holes, the Northern Irishman is not yet out of the tournament, but he must make up a lot of ground as he plays Kingsbarns on Saturday.
Fleetwood's impressive round included a run of five successive birdies on the back nine. He almost extended that sequence to six when a birdie putt from off the green on the 16th narrowly missed the hole. He might even have had an eagle on 15th, too, when his second shot at the par-4 bounced onto the green and hit the flag.
He finished his round in style by picking up his ninth birdie at the 18th.
Fleetwood, who became a father for the first time last week, was asked after his round how it felt to break the course record.
Fleetwood, 26, told Sky Sports: "It sounds good doesn't it? You don't really think too much about it when you are playing, but then I holed that one on the last and they said it was a course record. So, all in all, it was a good day's work!"
Dunne slipped back after a bogey on his second hole but responded with six birdies before dropping another shot at the 17th.