McIlroy was stymied in his drive for the top spot last week when he was bested by Hunter Mahan in the final at the WGC-Accenture Match Play Championship.
But he improved his chances for another shot at No. 1 with his performance Saturday, finishing 54 holes at 11-under 199.
Tom Gillis, who started the day with a share of the Honda lead, fell into a second-place tie with 22-year-old Harris English after registering a 1-under 69.
English carded a 66 to end the round at minus-9.
Second round co-leader Justin Rose stumbled to a 1-over 71, good for a fourth-place tie with Keegan Bradley (68) and Brian Harman (69) at 7-under 203.
Tiger Woods shot a 1-under 69 and is tied for 18th at minus-2.