Austin had birdied three holes in a row starting at the par-3 11th, cutting down Woods' lead to just one stroke after the eventual champion lipped out a five-foot par putt at the par-3 14th.
"I was trying to get them going crazy for someone else to let him know somebody else was out here," Austin said. "I got back in it. It was just a great day."
But Woods answered by sinking a 12-foot birdie putt at the 15th, pointing at the ball as he walked to the cup just as he did in 1999 after sinking a key putt to hold off Sergio Garcia down the stretch and win his first PGA crown.
That lifted Woods to eight-under par, two ahead of Austin, and the two traded pars to the finish, with Woods taking home the $1.26m top prize.
Austin fired a 67 for his first top-10 finish in a major and Els had a 66 to take third.
Canada's Stephen Ames, who began the day in second place three strokes back, soared to a 76 to finish 10 strokes behind Woods.