The Englishman was at 12-under 132 after seven birdies in the second round of the tournament played at Carnoustie, Kingsbarns and St. Andrews. Sweden’s Martin Erlandsson was second after five birdies in a 68 at Carnoustie.
Parry is coming off his first European Tour victory, at the Vivendi Cup two weeks ago.
“It’s a confidence thing especially after that win knowing that you can finish the job off and that’s how I have pushed on now,” the 24-year-old Englishman said. “I like to say that this I feel has been coming for some time.'
“I made five cuts in a row before the Vivendi event. I was striking the ball well then, but in my last two events I have started holing putts and I hope it continues over the weekend.”
While the Vivendi tournament drew only one player ranked inside the top 84 in the world, the Dunhill Links field includes nine members of Europe’s winning Ryder Cup team.
Ryder Cup players Ross Fisher of England shot a 68 and Martin Kaymer of Germany had a 69 for a share of third place at 7 under alongside Alvaro Quiros of Spain (69). All three played at St. Andrews.
Graeme McDowell, who provided the winning point for Europe at Celtic Manor, was alone in sixth at 6 under after making a 20-foot birdie putt on No. 18 for a 68 at St. Andrews.
Padraig Harrington of Ireland, another Ryder Cup player, was another shot back after a 68 at St. Andrews. He could have done better after four early birdies, but found the course more difficult when a cold wind started to blow during the second half of his round.