SAN ANTONIO, March 29, 2014 (AFP) - Bowditch, who is seeking a first US tour title, had a 54-hole total of 12-under par 204.
He was three strokes in front of Americans Matt Kuchar and Andrew Loupe.
Kuchar fired a seven-under 65, the low round of the day, for 207. Loupe could have had sole possession of second place, but bogeyed his last hole for a two-under 70.
American Pat Perez was alone on 208 after a 69 and American Kevin Na's 69 left him on 209.
Bowditch chipped in at the first two holes for a birdie and an eagle. He added two more birdies and just one bogey, at the par-four ninth, to build on his 36-hole lead.
"I actually hit two good shots on the first hole, I was just sort of in between clubs for my second," Bowditch said. "It was probably the easiest chip you're going to get out there. It landed on the front and let it run out.
"The second hole was a little different. I took a bit of a risk out of the bunker for my second shot to try and get it pretty close to the green and the lie was good.
"I was just trying to chip it up there around a comfortable tap-in distance so I got lucky and it dropped in."
That bit of luck proved especially helpful since Bowditch was scrambling much of the day, finding only eight greens in regulation.
Bowditch's best finish this season was a tie for 19th at Pebble Beach. His best career finish on the PGA Tour was a tie for second at the Greenbrier Classic last year.
Bowditch had never even held the lead after a round in a PGA Tour event until this week.
Now he's poised to strike for a victory that would earn him a trip to the Masters, where compatriot Adam Scott will be defending the title.
"I'm just going to take it one shot at a time, one hole at a time," Bowditch said of his Sunday strategy. "That's all I can do. Hopefully have a fun day out there, find a lot more fairways and greens, make it a bit easier."
Five-time major champion Phil Mickelson got a Masters scare on Saturday, however, withdrawing after 10 holes saying he had pulled an oblique muscle on a tee shot.
"It just killed and it wouldn't subside for 10 or 12 seconds," said Mickelson, who was one-over for the day at the time, and wary of exacerbating the injury with the first major of the year starting at Augusta National on April 10.
"I'm going to go back to San Diego for a couple of days and have a doctor take a look at it, but there's really not much you can do for a pulled muscle," said Mickelson, who added he didn't know if he'd be able to start as planned next week at the Houston Open.
Leading third-round scores on Saturday in the $6.2 million (4.5 million euros) US PGA Tour Texas Open (USA unless noted):
204 - Steven Bowditch (AUS) 69-67-68
207 - Matt Kuchar 70-72-65, Andrew Loupe 67-70-70
208 - Pat Perez 68-71-69
209 - Kevin Na 70-70-69
210 - Daniel Summerhays 72-68-70, Chad Collins 71-66-73
211 - Ryan Palmer 72-71-68, Zach Johnson 70-71-70, Will MacKenzie 69-72-70
212 - Jim Furyk 70-74-68, Geoff Ogilvy (AUS) 74-69-69, Jerry Kelly 71-71-70