Woods, a 15-times major champion, and two-time Super Bowl winner Manning jumped out to a three-hole lead on the front nine at the Medalist Golf Club in Hobe Sound.
While Woods's booming drives and Manning's solid putting saw the pair dominate the early holes, five-times major winner Mickelson and Brady won the 11th and 14th to shave the lead to one.
However, they were unable to force extra holes after Woods delivered a dagger putt on 18 as darkness descended on his home course.
