The first round was suspended for darkness, but the start of the tournament was delayed for several hours as heavy rain pounded Firestone Country Club. Officials decided to change the tee times and sent the players off in threesomes off both the first and 10th tees.
During the round, there was another delay thanks to a thunderstorm in the area. Play resumed and 16 of the 76 players in the field completed their first rounds.
The remaining players will come back to Firestone at 7:30 a.m. ET Friday morning to complete the first round.
Cink is 5 under through 10 holes, while Rod Pampling, the winner of the International two weeks ago, is 4 under par through 12 holes.
Tiger Woods, a three-time NEC Invitational champion, is fighting to keep his No. 1 ranking. This week, he broke Greg Norman's record for most weeks atop the rankings with 332, but there are several scenarios where PGA champion Vijay Singh or Ernie Els could overtake him. Woods responded on Thursday.
He is 3 under par with one to play, but was tied for the lead until some late miscues. Woods bogeyed 16 and 17, both times missing putts inside 10 feet, and is tied with Zach Johnson and Carlos Franco, who are both early on their back nines.
'I was feeling I was playing well and throwing away too many golf shots,' said Woods, who won this event from 1999-2001. 'When you make seven birdies on this golf course, that's not easy to do, and then you throw it right away with four bogeys, that's not very good.'
Woods, who bogeyed the first but responded with three birdies in a row from the second, holed out from short of the green at the ninth and made it to 2 under par. He added birdies at 12, 13 and 15, but dropped a pair of shots late in his round.
Singh, playing in the first group out on the back nine Thursday, struggled after his third major title. He bogeyed two of his first three holes, but got it back to even par when he played his final two holes.
At the eighth, Singh landed in the right bunker and could not get up and down for par. One hole later, Singh drove into the left rough and tried to hack it out and left it short. He left it short of the green again, chipped on and made the putt for a double bogey.
All totaled, Singh carded a 3-over 73.
'The high was really last week, and now I've got to get over it and start a new week,' said Singh, who defeated Justin Leonard and Chris DiMarco in a playoff last week at Whistling Straits. 'It's not an excuse, but it does kind of affect you a little bit.'
Els is 1 under through 11 holes with two birdies and one bogey.
As Singh and Els are chasing Woods for first in the World Rankings, Woods will be chasing his new Ryder Cup teammate Friday morning.
Cink, who was added to the team Monday morning and will be participating in his second Ryder Cup, began on the back nine Thursday and tallied four birdies in his opening nine holes.
At the 10th, Cink drained a 7-footer for birdie to go one clear of Pampling. Did his recent piece of good news impact how he played in his first round since the selection?
'It didn't hurt but I don't think it really had any effect,' said Cink, who moved up the Ryder Cup table with top-10 finishes at the Buick Open and the International. 'I'm obviously glad I've been picked and it's nice to start out in this tournament right after that, but it really is more of an indication of the way I've been playing for the last couple months than just one pick.'
Pampling recorded four birdies through his first seven holes, including an 8-footer at No. 7. He mixed a birdie and a bogey the rest of the way and was on the 13th fairway when the horn sounded.
'It was a long day,' said Pampling. 'Everybody was kind of waiting around, but I got off to a nice start, made some nice putts and just kind of held it there.'
Jim Furyk, who lost this event in a playoff to Woods in 2001, shot a 2-under 68 and is tied with Davis Love III and Frenchman Thomas Levet. Shigeki Maruyama is 2 under through 16 holes, DiMarco through 15, Sergio Garcia through 14 and David Toms is making the turn at minus-2.
Phil Mickelson played poorly on Thursday. He drained an 18-foot eagle putt at the second, but attempted a risky shot from the rough at three and splashed in the water. He made double bogey at that hole and bogeyed nine and 13. The Masters champion is 2 over through 14 holes.
Defending champion Darren Clarke is also 2 over and will be playing his 17th hole Friday morning.