Woods got his third round under way at seven under par in Minnesota in the knowledge he had not lost the eight Major Championships he had led at the halfway stage and with a four shot overnight lead the World Number One had threatened to turn the final Major of the year into a procession.
Defending champion Harrington had reeled in Woods' lead as the final groups neared the clubhouse, but having been caught, the 14 time Major winner was sparked out of a nine hole run of pars with a birdie at the 14th.
Then Harrington bogeyed the 18th for a third round, three under par 69 and Woods returned to grind mode and parred his way home for a one under 71, at eight under two strokes ahead of the Irishman and Korea's Y E Yang €" his 67 the low score of the day.
Henrik Stenson of Sweden and US Open Championship winner Lucas Glover will start the final round at four under after rounds of 68 and 71 respectively with Denmark's Sren Kjeldsen and Ernie Els of South Africa at three under, both having shot 70s.
In total eight European Tour Members finished the day among the top 12 with Harrington and Yang leading the way.
€I was just trying to be very patient out there,€ Woods said. €The golf was playing a little more difficult and I had the lead so I played conservative.
€I didn't give myself a lot of looks and the one putt I missed was the three putt (at the fourth) so other than that it was a really good, solid day.€
Harrington was left a little deflated after his closing bogey. €It was a little disappointing,€ he said. €Sometimes when you get off to a shaky start and make a few pars you do feel better for it.
€Then I did start playing well and I holed a few putts and I was feeling good about things. Then at the end I got a flyer out of the rough and it was a disappointing way to finish.€
Harrington had started the day as part of a five man group four shots behind Woods that also included Glover, England's Ross Fisher, Australian Brendan Jones and two time winner Vijay Singh.
Glover birdied the par four second to close the gap before Woods, chasing a third victory in as many weeks also birdied the hole to return his lead to four.
It was short lived, though, as Woods bogeyed the first par three at the fourth and Lee Westwood moved within three after birdies at the second and seventh, only to then double bogey the par-three eighth and fall back to two under.
Former HSBC Champions winner Yang also got to four under having started at one under and Harrington was the next to get there, the Irishman sinking a birdie putt at the seventh from eight feet and another at the eighth from 18 feet.
Glover joined Harrington on five under with a birdie at the seventh and Singh, having bogeyed the sixth, made his first move in the right direction with an eagle three on the seventh, chipping in from the fringe as Woods worked hard to save par for the third hole in a row.
Glover misfired for the first time at the tenth, short siding himself in a greenside bunker and taking bogey to go to four under as Els chipped in for birdie at the 12th to take his place at five under, while playing partner Kjeldsen bogeyed to slip to four under.