Marcus Fraser, of Australia, and Matt Wallace, of England, shot 68s in high winds at Carnoustie and St Andrews, respectively.
"It was brutal out there," Fraser said. "Doesn't really matter if it's into the wind or downwind, and then you get the cross-breeze off eight and nine. That's as strong as I've played the golf course, I think."
All 168 players in the field will play a round on each course, before the final round takes place at St Andrews on Monday.
Hatton is one of two European Ryder Cup-winning stars playing at the Dunhill Links. The other, Tommy Fleetwood, shot 71 at Kingsbarns.
Only 24 players broke par in the tricky conditions - including Kiwi Ryan Fox.
Partnering former Australian cricketer Shane Warne, Fox carded a one-under opening round 71 to sit in a tie for 15th, three shots off the lead.
- AP