Following on from his maiden victory in the Vivendi Cup 2010 two weeks ago, Parry birdied the 11th and 16th at St Andrews for a back nine 34.
That left him seven under for the week after an opening 67 at Kingsbarns in the three-course Pro-Am format.
Alongside him was Dutchman Maarten Lafeber, who had formed part of a four-way tie at the top overnight on six under.
Despite dropping a shot at the 12th - his third - at Kingsbarns, the former Dutch Open winner birdied two of his next four for a share of the lead.
Seven players were tied for third, including the other three overnight co-leaders - Thomas Björn, Ricardo Gonzalez and Martin Laird.
They were joined by Spain's Alvaro Quiros and English pair Ross Fisher and Simon Dyson at St Andrews and Swede Martin Erlandsson at Carnoustie.