Woods, who began another windy day at Hazeltine with a four-stroke lead over a group of five players, shot one-under-par 71 for an eight-under total of 208.
The 33-year-old American has never lost when he has carried a lead into the final round of a major, and all 14 of his major championship victories have come in this fashion.
While challengers were piling up birdies, and bogeys, Woods had 15 pars, two birdies and one bogey and finished just before heavy rain hit the area.
Holder Harrington, who briefly tied Woods for the lead late in the round, shot 69 despite a bogey at the last hole, and Yang fired a five-under 67 to match Woods's first-round score and lowest for the tournament.
Four strokes behind Woods, tied for fourth on four-under, were US Open champion Lucas Glover and Sweden's Henrik Stenson. American Glover had 71, while Stenson posted a 67.
Triple major champion Ernie Els, who stood one shot behind Woods before finishing with three successive bogeys, was joined by Soren Kjeldsen of Denmark a further stroke behind on 213. Yang, who won this year's Honda Classic on the US Tour, surged up the leaderboard with three successive birdies from the 14th. He had six birdies in all against one bogey and will be paired with Woods in Sunday's final round.
Meanwhile, a sub-par card continues to elude Jeev Milkha Singh, who turned in two-over 74 in his penultimate round to slip a rung to tied 49th.
With a 54-hole total of five-over 221, Jeev joined Fred Couples, Jim Furyk, Luke Donald, Justin Leonard and Jeff Overton at the 49th place and his quest for an automatic place in the Greg Norman-led International team for the Presidents Cup seems over since the Indian would require an improbable top-four finish for that.
