Simpson led by one stroke coming into the day, but built the cushion to two thanks to his finish at The Old White TPC, en route to a 5-under-par 65.
The U.S. Open winner completed 54 holes at 14-under 196, two better than Troy Kelly, who fired a blistering 8-under 62 and jumped into second place at minus-12.
Ted Potter Jr. carded a 6-under 64 for sole possession of sixth place at minus-10.
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