They had a one-shot lead over Xander Schauffele.
He said: "I feel like I'm sort of on a mission here".
Yet two-time FedEx Cup champion and BMW Championship victor Woods gave back two shots on his last two holes to shoot an even-par 70, leaving him eight-under after 36 holes, with McIlroy a shot better off after signing for a 69.
One day after a 62, Woods shot 70 and was five behind. He was one over through 8 before birdieing two of the next three holes to get to one under for the day and nine under for the tournament.
Australia's Dimitrios Papadatos leads by four shots on 16-under par thanks to a second successive, eight-under 63 with Sharvin tied 29th on five-under after a 66 and Galbraith three-under after a 70.
The top 30 players in the season-long standings after the BMW advance to the season-ending Tour Championship in two weeks.
On Friday at the BMW, he was the ultimate driving machine, hitting 11 of 14 fairways to eclipse his season average by more than 20 percent.
Thus, Shauffelle has started to move with the intention to win it all in the BMW Championship.
"I hit a lot of lovely putts that were on top of the edge and then obviously hit a couple bad ones on the last hole". Schauffele, hopeful that a victory will give US captain Jim Furyk reason to pick him for the Ryder Cup, stayed with Rose the whole way until he three-putted from the tight collar on the 18th hole for a bogey and a 67. I couldn't get the ball to the hole and when I did I was reading too much break.
At stake for Rose is moving to No. 1 in the world for the first time in his career.
Before you set your PGA Tour DFS lineups on DraftKings or FanDuel for the 2018 BMW Championship, you need to hear what Mike McClure has to say.
The same is true for Bradley and for Noren, the Swede who makes his Ryder Cup debut at the end of the month. He won that week for his 79th career victory on tour but is still stuck on the mark five years later.
Ian Poulter's chances of a Ryder Cup pick took a slight knock after missing the cut and falling seven spots into 45.