Cink and Henry finished with a 36-hole total of 20-under 122 in the best-ball tournament.
Faxon and Johnson led by two strokes at the turn when Cink and Henry went on the birdie binge.
Cink, who finished second with David Toms in the 2002 tournament, birdied 11, 13, 15 and 16. His 18-foot putt on the 15th hole gave his team a one-stroke lead it didn't relinquish.
'We really teamed up well,' Cink said. 'It wasn't like one guy struggled and the other guy was on fire. We both played pretty well.'
Cink and Henry also teamed up at last year's Ryder Cup and World Cup.
'Our games are very similar,' said Henry, a native of Fairfield, Conn. 'We hit the ball about the same distance. We have a lot of the same strengths. I think that's important in a format like this.'
Faxon, who founded the tournament in 1999 with fellow Rhode Islander Billy Andrade, finished second for the fifth time.
Both Faxon and Johnson, who won this year's Masters, had makable birdie putts on the 18th. Faxon's 15-footer rimmed the left side of the cup, while Johnson's 20-footer rolled three inches to the right.
'The juices were flowing on the last hole,' Henry said. 'Brad hit a great (approach) shot. Unfortunately, the putt dove left just short of the hole. Brad's always so dangerous, especially on this course. He's probably played it a thousand times.'
LPGA Hall of Famer Julie Inkster and Natalie Gulbis, the first all-female team to compete in the tournament, combined for 4-under 67 Tuesday and finished ninth in the 10-team field with a 9-under 133. Inkster and Gulbis recorded par on eight of nine holes on the back nine on Tuesday.
Cink-Henry, $250,000 60-62--122
Faxon-Johnson, $175,000 60-63--123
DiMarco-Villegas, $130,000 61-64--125
D. Quigley-B.Quigley, $130,000 63-62--125
Price-Clark, $115,000 63-64--127
Toms-Immelman, $110,000 65-63--128
Jacobsen-O'Hair, $102,500 67-63--130
Andrade-Trevino, $102,500 66-64--130
Gulbis-Inkster, $95,000 66-67--133
Choi-Parnevik, $90,000 68-68--136