Kuchar played bogey-free in a round of seven-under 63. He lost a chance to add one more birdie when he drove into a fairway bunker and narrowly cleared the lip.
Simpson reached the par-five 18th green in two for a two-putt birdie with his conventional putter. That gave him a 66 and a share of the lead at 12-under 128.
The top-ranked McIlroy threw his hands in the air and high-fived playing partner