Two weeks after winning the British Open, Woods stands at 12-under-par 132 through two rounds at Warwick Hills Golf and Country Club.
Tied with Quigley overnight at 13-under, Woods, the 2002 champion, bogeyed the par-5 16th Saturday morning to slide back.
Quigley carded a 6-under 66 on Friday to get to 13-under-par 131. He was one of the few players with afternoon tee times to complete his second round Friday.
The tournament has struggled to catch up following two weather delays during the first round Thursday.
Players who didn't complete their second rounds Friday returned to the course at 8 a.m. (ET) Saturday. The third round began at 11:13 a.m. with threesomes teeing off on No. 1 and No. 10.
Two-time defending champion Vijay Singh -- the only three-time winner ever at this event -- went 1-under on five holes Saturday morning and leads a group of four players who are tied for third place.
Joining Singh at 11-under 133 were Jeff Sluman (67), Bo Van Pelt (66) and first-round leader Mike Weir (70).
Jim Furyk leads a group of seven players who share seventh place at minus-10.
When play was completed Saturday, the cut line fell at 3 under. Among those who will miss the weekend are Chris DiMarco, who finished second to Woods at Royal Liverpool, and David Toms.