In the 36-hole tournament for major winners, Retief Goosen shot a par 70 and fellow South African Trevor Immelman was at 6-over 76 in a strong wind at Mid Ocean Club in Bermuda.
Harrington, the PGA and British Open champion this year, birdied three of the last five holes.
There were times when you couldnt get at the pin from certain places on the fairway, and understanding how to shape the ball in the wind was essential, Harrington said.
Furyk, in the field for the injured Tiger Woods, made the turn at even par, then eagled the par-5 11th with a 6-iron from the fairway within four feet. But he bogeyed the 14th and made birdie on the last hole to catch Harrington.
Goosen, replacing Phil Mickelson, started with seven straight pars, and birdied the par-4 eighth. But bogeys at 9 and 17 offset a birdie at 10.
I think I had 34 putts today, Goosen said. Nothings going in at the moment, so I just have to work on that and hope that it comes back.
Immelman, the Masters champion, endured a miserable back nine which included double-bogeys at Nos. 11 and 16.
First place in the select field is worth $600,000, while fourth place pays $200,000.
Angel Cabrera defeated Harrington in a three-hole playoff last year.