Oosthuizen held a five shot lead over 1989 champion Mark Calcavecchia when the delayed second round was completed, the South African making the most of his early start on Friday before the bad weather struck.
The 27 year old added a 67 to his opening 65 for a halfway total of 132, 12 under par, setting a clubhouse target which was never in danger of being threatened once winds gusting over 40mph whipped around The Old Course in the afternoon.
Rock was among the players who made the cut right on the mark of two over par, but raced to the turn in 31 with birdies at the first, sixth and ninth, along with an eagle on the seventh where he holed his second shot from the fairway.
At three under par Rock was still nine adrift of Oosthuizen, but was at least showing what was possible.
Lee Westwood and Paul Casey were six off the pace on six under and out in the penultimate group at 4:30pm, with Tiger Woods two shots further back and paired with Northern Ireland's Darren Clarke.
Clarke's compatriot Rory McIlroy, who shot an 80 after leading the way with a record-equalling 63 in the opening round, had parred the first three holes to remain one under.
Rock dropped his first shot of the day by missing from three feet for par on the 17th, but made amends by holing from six times the distance for a birdie on the last.
The resulting 67 saw him set the early clubhouse target at three under par, although Ross Fisher looked set to overhaul that after moving four under with a birdie on the 15th.
It was still more than two hours before the leaders were due out, but the blustery wind showed no sign of easing up for the later starters.