Mediate and Janzen recorded 12 birdies, including five in a row bridging the front and back nine, and overcame a one-shot deficit.
"We're in the lead because we both picked it up when the other wasn't there," Mediate said.
The teams will compete in a scramble format in Sunday's final round as they vie for the $500,000 first prize in this unofficial PGA Tour event.
"This is the best place to be, but we still have to play exceptional golf tomorrow," Janzen said.
Huston and Maggert recorded a second straight 8-under 64.
This marks the third Shootout appearance for both Huston and Maggert, who have combined for eight titles in more than 600 PGA Tour appearances. The two played together at the 1994 Presidents Cup, losing to Vijay Singh and Steve Elkington.
O'Meara, who won the inaugural tournament with Curtis Strange in 1989 at the Sherwood Country Club, and Cook were tied with Matt Kuchar and David Gossett, who shot a 64, and Dudley Hart and Jeff Sluman, who carded a 62.
Two-time defending champions Scott McCarron and Brad Faxon were 10th in the 12-team field at 134.