Bernhard Langer finished alone in third at 12-under-par 204. David Toms carded a 4-under 68 to finish one shot further back at 11-under-par 205 alongside Nick Price.
Harrington dominated the par-5s at Sherwood Country Club in taking the outright lead. He got started with a 12-foot eagle at the par-5 second.
He birdied the third but ran into trouble with a bogey at the fourth. At the par-5 fifth, the Irishman played his second shot short but holed out from the fairway for his second eagle of the day.
Harrington made the turn at 13-under and knocked his approach inside four feet for a birdie at the 10th. At the par-5 11th, Harrington's second shot nearly found the bottom of the hole and stopped within two feet of the cup. He tapped in for his third eagle of the day.
At the par-5 13th, Harrington reached the back fringe in two and almost had another eagle but his putt lipped out. He settled for birdie and made a three-foot putt at the 16th to reach 18-under.
Harrington then hit his second shot to eight feet at the 17th and drained the putt en route to a new 54-hole tournament record.
'Shooting 70 in the last round to win the tournament is better than shooting 63 and the course record on the third day if it doesn't come to anything,' said Harrington. 'Maybe if I win the tournament, I will put it down as the best round. At the moment it is not.'
Harrington, who finished second on the European Tour's money list this year, was eager to play alongside Woods again in the final round.
'I am happy with that,' said Harrington. 'I am sure he wants to be with me to try and put some pressure on. I am not one to watch scoreboards, so I am quite happy to try and manage my game.'
Woods had trouble with the putter early on, failing to save par from inside four feet at the third and fourth holes. He recovered with a two-putt birdie at the fifth and dropped his approach inside two feet at the seventh to make it two in a row.
Woods struggled around the turn with a bogey at the ninth and dropped another shot at the 10th after he could not get up and down from off the green.
At the par-5 11th, Woods reached the green in two and two-putted for a birdie to move to 11-under. He bogeyed the 13th but countered with two birdies down the stretch.
'It was a sloppy round of golf,' said Woods. 'I didn't play particularly well, and it showed. I made too many mistakes and didn't make any putts early in the round, which was the key because I needed to try to keep pace with Paddy.'
Jim Furyk and Colin Montgomerie share sixth place at 10-under-par 206. Davis Love III, who won this event in 2000, was alone in seventh at 9-under-par 207.
Phil Mickelson shot a 4-under 68 to finish alongside Retief Goosen at 6-under-par 210.
Chris DiMarco finished alone in 11th at 5-under-par 211 while Vijay Singh and Michael Campbell were one shot further back at 4-under-par 212.
Mark O'Meara is 14th at three-under-par 213 followed by Bob Estes at 1-under-par 215. PGA Championship winner Rich Beem is last at 5-over-par 221.
More from the Target World Challenge: