The 31-year-old Welshman added a six-under-par 66 to his opening 68 to establish a two-stroke lead over last year's runner-up, Bernhard Langer, before a thunderstorm brought the proceedings to a halt.
When the storm had subsided, another Briton, Mike McLean, took advantage of the docile conditions to take a share of second place and move to eight under par alongside Langer, while Ireland's David Feherty made a positive move with a 68 for 139.
Mouland's extraordinary low putting count with a Ping putter - just 20 shots - rather than his 10-under-par 134 total sent a disbelieving buzz around the course.
'That was just incredible,' Mouland said. 'I hadn't used this putter for five years and it was lying with about 50 others in a bag at home.
'I won my first tournament with it, the Car Care International in 1986, and discarded it soon afterwards. I was going through the bag last week and decided to try it again.'
Greg Norman who shot a 69 to finish three behind Mouland on 137, raised his eyebrows in astonishment and Langer admitted he could ever not remember taking less than 22 or 23.
Spain's Jose Maria Olazabal, third in the Open at Muirfield, missed the cut with a 74.Reuse content