Haas fired a five-under par 67 while Cink, who has not won since defeating Tom Watson in a playoff at the 2009 British Open, shot a 68 to stand atop the leaderboard on 11-under 205, both nine strokes ahead of World No. 2 McIlroy.
Steve Wheatcroft, who booked his place in the field in a Monday qualifier, topped the leaderboard with a second-straight 67 for 10-under par 134.
Juan Monaco indicated he will be a threat to the big-name players at the upcoming French Open by claiming his second clay court title of the season with victory at the U.S. Men's Clay Court Championships.
US second seed John Isner outlasted Spanish third seed Feliciano Lopez 6-7 (5/7), 7-6 (7/4), 6-3 on Saturday to reach the final of the $442,500 ATP US Men's Clay Court Championship.
South African Louis Oosthuizen posted a second straight 66 on Saturday to take a two-shot lead over Hunter Mahan after three rounds of the US PGA Tour's $6 million Houston Open.
England's Brian Davis and South African Louis Oosthuizen shared the clubhouse lead on Friday as darkness stopped play in the second round of the rain-hit Houston Open.
Defending champion Phil Mickelson, resuming his rain-disrupted first round, seized a share of the lead on Friday at the Houston Open with a seven-under par 65.