Green is 15-under 198 through 54 holes and withstood pushes by 2006 Masters runner-up Tim Clark (66) and Jonathan Byrd (65). Clark is 14 under after finishing with three straight birdies, and Byrd was two strokes off the lead.
Green, a 32-year-old from New South Wales, Australia, had never led a PGA TOUR event after two rounds until he shot 63 on Friday to go 12 under. That gave him a one-stroke lead over Carl Pettersson and Jason Dufner, and the momentum carried into the third round.
He drove a 145-yard approach shot within five feet of the cup on No. 5, setting up his second birdie of the round. He also birdied the sixth and eighth holes to go 16 under, before bogeying 11 and 12. That put him at 14 under and, momentarily, in a tie with Byrd.
Green recovered with birdies on 13 and 14, but a chip shot on 17 sailed over the green. Then, he tried to putt up a slope but the ball stopped short of the green. He bogeyed the hole, leaving him one shot ahead of Clark.
Some late drama aside, Green is in a good spot.
He spent the past three weeks relaxing back home in Australia after missing the cut at the U.S. Open. Now, he's trying to become the third Australian in four years to win the Deere, joining Mark Hensby and John Senden.
Byrd, who won the 2002 Buick Challenge and took the B.C. Open two years later, had trouble on the final two holes.
He saved par on 17 after sending his tee shot into the rough on the right, but couldn't do the same on 18. This time, he wrapped his second shot around an oak tree and into the water to the left of the green, settling for what he called a 'great bogey.'
'I guess everybody's game is an adventure,' Byrd said. 'I know Tiger's is at times. That's just golf. You hit spots and try to find a way out of it, get creative.'
With the British Open next week, most top golfers skipped this event, and the Deere lost one major draw last month and another on Friday. First, Michelle Wie withdrew because of wrist injuries. Then, Masters champion Zach Johnson missed the cut.
With the 15th-ranked Johnson out, the only top 50 player left in the field was Pettersson at 46, but it became clear early on that he wasn't going to make a move. He was 3 over for the day before finishing with a 71.