The Irish duo hit eight birdies to finish the third round with an 8-under 64, and a 21-under total of 195 at the Mission Hills complex.
However, the second-ranked McIlroy and 2010 U.S. Open champion McDowell will be unable to rest easy Sunday with Germany, South Africa and the United States all tied for second at 197.
Martin Kaymer and Alex Cekja made 11 birdies in their 11-under 61 on the Blackstone course carved out of cooled lava rock.
“We saw the scoreboard on the sixth green and we saw Germany were off to a flyer,” McDowell said. “We actually expected that today. We are probably a little disappointed that we couldn’t pick up a couple more shots on the way in. We really could have put a little bit of daylight between us and the chasing pack.”
McDowell did not need reminding about what the Ireland team faces on Sunday.
“We are going to have to go and play well tomorrow – it’s as simple as that,” he said.
“Today was a great day. We ham and egged it pretty well,” Woodland said. “Matt really got us going early. I was kind of all over the place, and he made a birdie on the first hole and got the edge off – and then made three or four in a row. I was struggling and he picked me up.
“Fortunately, I made some putts on the back nine. Hopefully gives us a lot more momentum going into tomorrow.”
Australia slipped to fifth place with a 198 as Brendon Jones and Richard Green on the wet and humid course had a 67.
Edoardo and Francesco Molinari put defending champion Italy back into contention with an 8-under 64 that left them tied for seventh with Mexico at 16 under.
But Ian Poulter and Justin Rose of England saw their hopes of lifting the trophy slip in the inclement conditions, with two bogeys in their 4-under 68. They have a share of 15th with Zimbabwe at 13 under.
Zhang Xinjun and Liang Wenchong of China were at 12 under.
Sunday’s final round of the $7.5 tournament will see a return to the tricky foursomes alternate shot format.
The World Cup features 28 teams and is being staged biennially following golf’s inclusion in the Olympics for 2016.
Golf Channel airtime: Saturday 10:30 p.m.-3:30 a.m.