The lightly regarded American duo shot a 6-under 66 on Saturday, giving them a one-stroke lead over France (62) and Scotland (66) going into Sunday's final round at the Mission Hills Golf Club in southern China.
They are 20-under 196 and have led after all three rounds.
Scores dipped on a warm, sun-drenched Saturday with teams playing the easier fourballs (better-ball) format. Sunday will be tougher playing foursomes (alternate-shot) in what is still a stroke-play event.
South Africa (66) and England (67) were two strokes off the lead. Argentina (64), the Netherlands (65) and Germany (66) were three behind.
Weekley and Slocum said they struggled all day with firm greens, tough pin placements and a swirling wind. In addition, neither made many putts. The exception was Weekley's eagle 3 on No. 3, where he hit a 4-iron to 15 feet and then dropped the uphill putt.
'It was just a tough day overall, it was a grind out there,' Weekley said. 'It wasn't like the first day when we hit it in there close and made some putts.'
Said Slocum: 'We survived with both of us not playing our best golf. So we have to feel a little fortunate.'
After jousting with France for the lead, the United States moved to 20 under for the tournament -- and a one-stroke lead over the French -- with Slocum's birdie on No. 13.
Weekley was chosen to play in the event after 13 other higher ranked Americans players declined. He then picked Florida high school friend Slocum as his partner. Both players have already won more than $2 million this season, and they'll each get $800,000 if they clinch victory here.
Scotland went to 19 under when Colin Montgomerie dropped a 12-foot birdie on the 18th. Montgomerie and Warren were the runners-up last year against Germany's Bernhard Langer and Marcel Siem. They did not return to defend.
The French pair of Raphael Jacquelin and Gregory Havret moved into contention with a 62 after starting the day five strokes behind the Americans. Havret had an eagle on No. 9, which helped to propel them up the leaderboard.
Both French players are part of a modest campaign to make golf more popular at home.
'This kind of result can definitely change things in France,' said Havret, who turns 31 on Sunday.
'The World Cup of Golf is very important to us because it's an international name,' Havret said. 'You know, if you win in Italy or Spain -- or whatever the tournament -- it's just the Open of the country. The World Cup means a lot in any country.'
The World Cup was prestigious years ago with winners like Jack Nicklaus, Ben Hogan, Sam Snead and Arnold Palmer, but lost much of its status recently without big-name winners. Woods won back-to-back in 1999 and 2000, and Retief Goosen and Ernie Els of South Africa won in 2001.