Trevor Immelman finished two shots back at 14-under-par 199 after a round of 68. He was followed by first-round leader Lee Westwood, who posted a 5-under 66 to move to 13-under-par 200.
Despite struggles on the back nine, Harrington played well enough to come out on top at Club de Campo, the site of his maiden European Tour victory. After Maarten Lafeber, who held a one-shot lead after the completion of the second round, bogeyed the second to create a four-way tie, Harrington hit a tremendous second shot at the par-5 fourth.
He was left with seven feet for eagle and drained the putt to open a quick two-shot lead. Harrington continued to plug along and knocked his approach to 15 feet for birdie at the sixth. He made it two in a row with a birdie at the seventh, but bogeyed the eighth after an errant drive.
Harrington recovered with a four-foot birdie at the 10th to regain the outright lead at 15-under. However, the Irishman was soon joined atop the leaderboard by Tinning, who ran home a birdie at the last for a brilliant 62.
Scott soon made his presence known as well. After a bogey at the third, the Australian collected five birdies over the next six holes to make the turn at 14-under. When Scott birdied the 14th, the lead belonged to three.
At the 15th, Scott took sole possession of first. He hit his second shot to six feet for birdie and extended his lead to two strokes over Tinning with a birdie at the 16th.
Meanwhile, Harrington was struggling at the par-5 14th. He missed the green with his approach and his chip shot hit a branch to fall short of the putting surface. Harrington's fourth reached the green, but he failed to save par to fall back to 14-under.
The 31-year-old persisted and birdied the 16th. He then sank a long birdie putt at the 17th to tie Scott, who bogeyed 17, at 16-under.
'My timing was all out on the back nine, but those two putts were very timely,' said Harrington. 'They made the round, to be honest.'
Scott's problems continued with a bogey at the last, leaving Harrington alone in first with one round to play.
Harrington, who is seeking his second victory of 2002, can move one step closer to capturing the Order of Merit title with a win at this event. Currently he trails Ernie Els and reigning Order of Merit champion Retief Goosen, but a matter of 18 holes can reverse the standings.
'I would not say I am buzzing with confidence,' said Harrington, who captured the Dunhill Links Championship earlier this month. 'I'm not sure whether rest or practice is the best thing to do now, but I'm going out there with a great chance to win.'
Nick O'Hern shot a 6-under 65 to finish four shots back at 12-under-par 201 alongside Jean-Francois Remesy and Des Smyth.
Goosen, who secured the 2001 Order of Merit title with a win at this event, was one shot further back at 11-under-par 202. He was joined by Soren Kjeldsen, Paul Casey, Andrew Coltart and Lafeber in a tie for ninth.
Full-field scores from the Telefonica Open de Madrid