Woods and Duval struggled in the opening-round fourball format but mastered it Saturday with a 9-under-par 63. That moved the American duo to 19-under 197 through 54 holes.
Woods and Duval, the world's first- and fourth-ranked players, shaved two strokes off the lead Campbell and Smail built on Friday. But the tandem from New Zealand birdied the final hole to cap a 7-under 65 and move three shots clear of the field.
Sunday's final round will return to foursomes, a format under which Campbell and Smail combined for a tournament-best 66 on Friday.
Four teams are tied for third at 18-under 198, including the South African tandem of Ernie Els and Retief Goosen, who have combined for three U.S. Open titles. Also within four shots of the lead are local favorites Toshimitsu Izawa and Shigeki Maruyama of Japan, Raphael Jacquelin and Thomas Levet of France and Angel Cabrera and Eduardo Romero of Argentina.
But Campbell and Smail know they have to be wary of Woods and Duval, who combined for six wins on the PGA Tour this season.
"I think the bottom line is, expectations for tomorrow are for the USA team to win," Campbell said. "You ask the media, anybody. But we've got a mission tomorrow, David and I, just to turn things around maybe and just go out and play.
"I've played with Tiger and David (Duval) a few times and I know it is going to be a bit of a circus out there and a lot of noise, which is normal. You just have to play your own game and just go out and play and forget about what Tiger and David are doing."
Last year, Woods and Duval overcame host Argentina, which was represented by Cabrera and Romero, to capture the inaugural event.
The World Cup is the fourth event in this year's World Golf Championships. Woods won the last of his five 2001 titles at the WGC-NEC Invitational in late August. He tied for 13th at the season-ending Tour Championship.
The winning team will share $1 million -- one-third of the total purse.
Swim Week Miami Beach 2014 [PHOTOS]