Green posted a 4-under 67 Saturday at Fontana Golf Club to complete 54 holes at 15-under-par 198.
England's Richard McEvoy climbed into a second place at 12-under-par 201 thanks to a third-round 64. Miguel Angel Jimenez and Steven Jeppesen each shot 69 on Saturday and share third place at minus-11.
Green is on track for his first win since claiming his lone European Tour title at the 1997 Dubai Desert Classic. He got off to a steady start with eight straight pars.
Martin Erlandsson, who played in the final pairing with Green, birdied the third to join Green in the lead at 11 under. Erlandsson had several chances to grab the lead on his own, but could not convert.
The 36-year-old Green finally got on the board with a birdie on the par-5 ninth. Around the turn, he rolled in consecutive 9-foot birdie putts from the 12th to move to 14 under, two clear of McEvoy.
Green parred his next four holes to remain there. At the par-5 18th, Green two-putted for birdie to finish three clear of the field as he has played the 18th at 4 under through three rounds.
'I feel comfortable on the course, it suits the way I like to putt,' admitted Green. 'I'll be fairly anxious to win because it's been a long time, but I won't be desperate because I'm not going to put any undue pressure on myself. It's hard to put a finger on why I've not won again, but I do now have more self-belief.'
McEvoy jumped from a share of 14th into second with a solid round. He tripped to a bogey on the second to open his round, but came back with birdies on three and four.
The Englishman turned in 8 under thanks to birdies at six and nine. Four more birdies on the back nine moved McEvoy into second place at 12 under.
'It's a bit tough at times when they are going out and winning tournaments, especially Luke (Donald), and you remember being at their standard, but it does give you the determination to do it,' said McEvoy of his 2001 Walker Cup teammates Donald, Graeme McDowell, Nick Dougherty and Marc Warren.
McEvoy has had a tough start to his season as he has missed the cut in six of his first seven starts and eight of 11 overall.
Swedes Johan Skold and Michael Jonzon each posted 7-under 64s Saturday to move into a share of fifth place at 10-under-par 203. They were joined there by David Park (68).
Chris Gane (64), Jean-Francois Remesy (65), Gary Orr (66), Jarmo Sandelin (69), Shaun P. Webster (68) and Graeme Storm (69) are tied for eighth at minus-9.
Erlandsson stumbled on the back nine with a bogey on 15 and a double-bogey at 16. He slid into a share of 14th at 8-under-par 205.