Kondo bogeyed the par-4 second hole before recovering with birdies on Nos. 7, 8 and 11 for a 36-hole total of 5-under 137 at the par-71 Phoenix Country Club.
Swedens Henrik Stenson was a stroke back at 4-under 138 along with Thailands Prayad Marksaeng, Spains Gonzalo Fernandez-Castano and Japans Michio Matsumura, who all shot a 70 in the second round.
Defending champion Ian Poulter of Britain finished with a 73 and is tied for 44th place at 4 over.
Japans Taichi Teshima posted the days low round of 66 to move into a tie for sixth at 3 under, along with teen star Ryo Ishikawa (67), Shigeki Maruyama (68) and American Brandt Snedeker (71).
Overnight leader Paul Sheehan of Australia only managed a 73 and now trails Kondo by three strokes.
Ernie Els, the 1993 winner, fell to a share of 38th place at 3 over after a 73.
The $2.1 million event is one of the richer tournaments on the Japanese mens tour. Recent winners include Tiger Woods (2004, 2005) and Padraig Harrington (2006).