Hatton backed up a first-round 70 at Kingsbarns with a six-under 66 at Carnoustie, which is regarded as the toughest of the three courses that stage the tournament. Eight of Hatton's last 10 rounds at the Dunhill Links have been in the 60s.
Hatton was joined in a tie for third place on eight-under with first-round co-leader Marcus Fraser (68 at St Andrews) and Matthias Schwab (67 at St Andrews).
In benign conditions after the fierce winds from Friday dropped, Mikko Ilonen and Darren Fichardt tied Pavan for the low round of the day with nine-under 63s at St Andrews.
Fleetwood, who was part of Europe's Ryder Cup-winning team in France last week, shot 67 at Carnoustie.
Meanwhile, Danny Lee was just outside the top 10 after his second round at the opening event of the PGA Tour season in California.
Lee carded a four-under 68 to move to seven-under for the tournament.
The New Zealander was tied for 11th, three back from the lead shared by Americans Phil Mickelson and Ryan Moore.
Lee finished his round with an eagle, with five birdies and three bogeys also in the mix.
Elsewhere fellow-Kiwi Daniel Hillier moved into a share of 12th at the Asia Pacific amateur Champs in Singapore - five shots behind the leader. Lydia Ko battled to a two-over day at her Korean LPGA event, nine-over for the event and in 58th.
- AP