Cink followed his opening rounds of 66 and 64 with a 5-under 65 to reach 15-under 195 on the TPC River Highlands, the best 54-hole score of his career.
Heath Slocum (64) was second, and defending champion Hunter Mahan (67), Vijay Singh (64), Kenny Perry (65), Tommy Armour III (65) and Kevin Streelman (62) were 12 under.
On a day when 24 golfers shot 66 or better, 17 players ended up within five shots of the lead going into Sundays final round. The average score of 68.2 was the best ever for a third round on the course.
Cink expects to have to be at 20 under on Sunday to have a chance to win.
Some guys got hot and boom, theyre up there at double-digits under par, Cink said. I dont see any reason why it wouldnt be the same way tomorrow.
Cink is looking for his first victory this year after six top-10 finishes. He is ranked seventh in the FedExCup point standings, the highest ranking of any golfer who hasnt won a tournament. But he usually plays well here, on a course where he earned his first tour victory as a rookie in 1997.
Cink had dropped in a tie with Slocum after hitting his tee shot on 16 into the water, but rebounded with an 11-foot birdie put on 17, and hit an approach within 2 feet on 18.
I felt like I gained some momentum back and put myself in a good mind-set for tomorrow, Cink said.
Slocum, who shot a 65 last Sunday for the low round at the U.S. Open, said that play has carried over. He bogeyed two holes on the front nine, then adjusted his swing and hit all nine greens after the turn. He finished with eight birdies.
Definitely the putter has carried over to this week, he said. Im going to probably have to lean on it tomorrow hard if Im going to think about winning this golf tournament.
Singh began making a move on the par-3 fifth, knocking in a 52-foot birdie put from the edge of the green and eagled the next hole after putting his second shot 4 feet below the pin.
Singh appeared to be in position to birdie the 18th after hitting a tee shot 341 yards. But his wedge shot found a right-side bunker and he missed a 6-foot par put.
When I took off today, I needed 7, 8, 9 under to have a good chance tomorrow, Singh said. Im very close. I still have to go out there tomorrow and shoot a good number.
Course conditions have been almost perfect for the first three days of play. Rain Friday night kept the greens soft, and with little wind, players were again aiming for the flag.
Streelman, D.J. Trahan and Chad Campbell all went out early and shot 62, one off the course record.
On these greens, if you give yourself enough looks, eventually youre going to make some putts, and I finally did that, Trahan said. When youre stroking it well, you kind of feel like almost all your putts have a chance. Thats the way I felt today.
Trahan and Campbell were at 199, tied for eighth place.
Streelman, who led after the first round of last weeks U.S. Open, shot a 3-over 73 on Thursday and didnt expect to be here for the weekend. But he followed that up with a 63 on Friday.
I was very proud of the way I bounced back and then to back it up with a 62 is pretty cool, Streelman said.
The 125 over those two rounds set a tournament record for consecutive rounds, and was just one shot off the PGA Tour record set by Mark Calcavecchia in 2001 at the Phoenix Open.
With rain in the forecast Sunday afternoon, tournament officials decided to start the final round early, with threesomes going off holes one and 10 at 7:30 a.m.. The leaders were scheduled to tee off at 9:30 a.m. and the officials expect the tournament to be over before 2 p.m.
It makes the wake-up call a little bit earlier, Slocum said. But, I have a 6-month-old, so Ill be up.