With overnight leader Brandon Pieters not teeing off until the afternoon, Grace was able to take the lead as he advanced to ten under par for the week.
Having been six under for his opening round, the 22 year old birdied his second and third holes - the tenth and 11th - before handing the shots back with bogeys at the 16th and 18th.
But he birdied the third to spark his good run of gains - only a par at the fifth preventing five in a row.
At ten under he led by one from Scottish Qualifying School graduate Elliott Saltman.
Saltman, also six under after the first day, birdied four of his first 12 holes with a single bogey.
Austrian Markus Brier and Swede Fredrik Ohlsson had drawn level with Pieters on seven under after 12 holes.