Woods, who started the day with a one-stroke lead over Harrington, hit a 5-wood from 247 yards, then sank an 18-foot birdie putt to finish an otherwise forgettable day on a high note in miserable rain at the Phoenix Country Club.
'It was a huge way to escape the day, to end up tied with all the things that happened today,' Woods said.
'Shots like that third shot on 18, that's why he's the number one in the world,' Harrington said. 'As I said to him on the green, it was worth coming out for that one shot alone today.
'I feel I had an opportunity to get a two or three shot lead, so it's a little disappointing to be only tied.'
Japan's Shingo Katayama (71) was two shots back in third, followed by compatriot Takuya Taniguchi (68) another shot back.
Woods, who took a five-week layoff before contesting last week's HSBC Champions at Shanghai, is looking to join Japan's Jumbo Ozaki (1994-96) as the only golfers to win the $1.69 million event three straight years.
Woods had little to get excited about apart from consecutive birdies at the fourth and fifth holes. He had a couple of unlucky breaks, most notably at the par-4 No. 2, where his drive landed behind a tree in the middle of the fairway, forcing him to chip sideways and settle for bogey.
He also double-bogeyed the par-4 7th, where his approach shot buried in a bunker guarding the green, again forcing him to play away from the hole.
Woods regained some momentum on the last hole, after Harrington bogeyed the 15th and 16th when he had a chance to take a substantial lead.
Rain is forecast again for Sunday.
Justin Rose's round came apart with a triple bogey on the par-3 17th that left the Englishman four strokes back after a 72. It came just after a birdie on the 16th where his putt cradled on the lip of the cup for a good 10 seconds before falling in.
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