THOUSAND OAKS, California, Nov 30, 2012 (AFP) - Northern Ireland's McDowell had a 36-hole total of nine-under 135 at Sherwood Country Club, where 18 golfers are chasing a first prize of $1 million from the total purse of $4 million.
Bo Van Pelt, Jim Furyk and Keegan Bradley shared second on 138. Van Pelt posted a 68 while Furyk and Bradley both carded 69s.
Woods, who hosts the unofficial event for the benefit of his charitable foundation, thrust himself into contention with a run of four birdies in five holes starting at the ninth.
But he lost some traction with his second bogey of the day at 15 and signed for a three-under 69 for 139.
"I certainly hit the ball a lot better than I did yesterday, made a couple more putts," said Woods, who added that "a nice little groove hitting irons" was the key to his run.
Otherwise, Woods said the conditions on the rain-softened course were "tricky".
"The greens were so soft, and we had to hit so much club to try and take the spin off the ball ... but you know, all the par-fives were reachable with good drives, and a couple of pins you could use slopes to get the ball close."
McDowell won this tournament in 2010, capping an outstanding season that included his US Open triumph up the Pacific coast at Pebble Beach.
He hasn't won since, and admitted it would be nice to punctuate a season in which he finished equal second at the US Open and tied for fifth at the British Open with a win -- even in a non-tour tournament.
"I would love to compete and play well this weekend, you know, really to kind of put a little icing on what's been a mediocre year," he said.
"Despite the fact that I feel like I've played some decent golf this year, I really don't have a lot to show for myself, and this would be a nice way to finish."
That said, McDowell said he wouldn't put any pressure on himself, also cautioning that the course could yield plenty of low scores at the weekend.
"I still believe there's something particularly low out there this weekend for someone," he said. "Certainly, seven-, eight-, nine-under par is not out of the question on this golf course. It's very receptive, and the green surfaces have remained very pure as well. You can make some putts."
McDowell started quickly with three straight birdies.
After his lone bogey of the day at the par-four seventh, McDowell added four more birdies coming in on a course softened by overnight rain and further dampened by intermittent misty showers on Friday.
Van Pelt, who had three birdies in his first five holes, kept the pressure on with birdies at the par-five 13th and par-three 15th that briefly saw him seize a share of the lead.
McDowell, meanwhile, notched back-to-back birdies at 16 and 17, and Van Pelt fell back further with his first bogey of the day at 18.
Second-round scores on Friday in the $4 million World Challenge golf tournament (USA unless noted, par-72):
135 - Graeme McDowell (NIR) 69-66
138 - Bo Van Pelt 70-68, Jim Furyk 69-69, Keegan Bradley 69-69
139 - Tiger Woods 70-69
140 - Rickie Fowler 73-67, Nick Watney 67-73
141 - Jason Dufner 73-68
142 - Dustin Johnson 74-68, Matt Kuchar 73-69
143 - Brandt Snedeker 75-68, Webb Simpson 70-73
144 - Zach Johnson 74-70, Steve Stricker 73-71, Hunter Mahan 71-73
145 - Ian Poulter (ENG) 73-72, Bubba Watson 71-74
146 - Jason Day (AUS) 71-75