The pair, playing alternate shots, posted a six-under-par 66 for a one-stroke advantage over first-round leaders Jerry Kelly and Steve Stricker.
Charles Howell III and Rory Sabbatini, and Kevin Chappell and Kevin Kisner are four shots further back on 16 under.
British pair Luke Donald and Russell Knox slipped to tied eighth on 13 under after a 71.
Lexi Thompson and Bryson DeChambeau are 10th at 11 under after a 71.
Thompson is the second woman to compete in the event, following Annika Sorenstam in 2006.
The 12-team tournament, the last PGA Tour event of the year, is hosted by former world number one Greg Norman at the Tiburon Golf Club.
It features three rounds played in differing strokeplay formats over three days, with the pairs playing a scramble on Thursday and finishing with a better-ball format on Saturday.
Matt Kuchar and Harris English claimed the second-round lead at the Franklin Templeton Shootout in Florida.