Woods shot a 2-under-par 70 and was at 6-under 210 through three rounds, nine strokes behind Harrington.
Harrington also shot a 70, putting him at 15-under 201 to take a two-stroke lead over Northern Ireland's Graeme McDowell (68). Former U.S. Open champion Retief Goosen posted a 77 and Denmark's Mads Vibe-Hastrup had a 66 to trail by three strokes.
Woods does not like his chances at winning this event for the third straight time.
'Probably not, the way things are going,' Woods said. 'There are too many players out there. I think Paddy's going to have another good round and will move further away from me.'
Harrington had been putting well, but he settled for a round with a bogey and just three birdies.
'I'm pleased to have a two-stroke lead,' Harrington said. 'I came to the course today expecting not to be in the lead, if it was Tiger or someone else. But today, if I had a good putt, it didn't go in.'
On a sunny morning, Woods let one chance after another slip away with his putter, just missing birdie attempts of around 10 feet on the 12th, 13th and 18th holes. He finished with a quiet round of three birdies and a bogey.
'I haven't got anything going this week,' Woods said. 'It's hard to make low scores without making the putts.'
He is playing his first tournament since tying for 15th at the Masters a month ago. The Deutsche Bank, which he won in 1999, 2001 and 2002, is one of two events he will play before the U.S. Open starts June 12.
Woods rallied from 10 strokes back after the second round to catch Michael Campbell and win in 2001, but he was on the leaderboard when the New Zealander nearly equaled a record two-day low for the European tour.
The next day, Campbell self-destroyed with a 73 and Woods shot a 63 to catch him.
This year, Woods has been quiet. He fought high winds in the first round to start with a bogey-free 69. The following day, two early bogeys hurt him and he settled for a 71.
Woods started the third round tied for 28th. He has played the whole week with a new unnamed prototype ball he has helped develop instead of his usual Nike TW.
'It goes a little bit further and more than anything it's a lot better in the wind. I've noticed quite a bit of difference in the ball,' he said.
Woods was trying to become the first player on the European tour to win three straight titles in two events. He also won the WGC-NEC Invitational from 1999-2001.
Only Nick Faldo, Ian Woosnam and Colin Montgomerie have won three in a row, but only at one tournament.
'You know it's frustrating because I'm hitting good putts but there is nothing you can do about it,' Woods said. 'That's the way it is.'
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