But consecutive bogeys at his 16th and 17th holes put paid to that notion, before he birdied the par-five ninth after hoisting a five-wood second shot to the heart of the green.
Woods moved to seven-under par with a birdie at his 10th hole. He won that week for his 79th career victory on tour but is still stuck on the mark five years later.
Damp fairways and greens at Aronimink Golf Club presented endless birdie opportunities, but former world No.1 Day's lacklustre two-under-par 68 left him at 11 under and six shots back of the lead.
Two late bogeys stopped McIlroy from grabbing the outright lead.
"So, it was just one of those days you had to stay aggressive".
"I made a few putts today, right out of the gate". I get good support around here.
Tiger Woods walks to the 11th hole tee box during the second round of the BMW Championship golf tournament at Aronimink GC.
American Xander Schauffele, who is trying to impress Furyk enough to earn the final wildcard spot on the US Ryder Cup team - announced after this tournament on Monday - sits one shot behind the pair. I missed a couple of short ones and I felt the greens were a little slower today.
Leishman is projected to need at least a tie for 38th to remain inside the FedEx standings's top 30, who advance to the Tour Championship finale. "I wasn't doing much".
"I made some great putts out there today including getting off to a better start than I have most of the season", he said.
After a 293 yard drive on the 413-yard par-4 second, Steele chipped his fourth shot to 6 feet, which he rolled for one-putt bogey on the hole.
On the Challenge Tour, Ardglass's Cormac Sharvin and Whitehead's John Ross Galbraith were the only Irishmen to make the cut in the Bridgestone Challenge at Luton Hoo Hotel, Golf and Spa.