Harman, a lefty from Savannah, Ga., fired a 67 on Monday and now holds an eight-stroke lead over Matt Savage with a two-day total of 7-under-par 133.
Savage followed up his Monday round of 68 with a 3-over-par 73 and sits at 1 over for the championship.
The first round was completed earlier Tuesday morning following hours of heavy fog on Monday, which caused play to be suspended.
Match play will begin on Wednesday with the top 64 scorers competing.
Harman, who captured the 2003 title with an easy 5-and-4 victory, is looking to become only the second player in history to win this event in consecutive seasons. Tiger Woods captured three straight crowns from 1991-93.
'I don't even think I am playing my best golf, but I'm pretty confident,' said the 17-year-old Harman. 'I didn't come (here) to finish second.'
Sung Hoon Kang sits in third place with a two-round total of 142. There is a tie for fourth between Lucas Lee and Roberto Galletti Jr, both one back of Kang, while Charlie Harris and Seung-Su Han sit together in fifth at 144.