SAN ANTONIO, March 29, 2014 (AFP) -Bowditch fired a five-under-par 67 that included five birdies and an eagle at the par-four 12th hole -- where he holed out with a wedge from 83 yards.
His eight-under total of 136 gave him a one-shot lead over American Chad Collins, who carded a 66, and rookie Andrew Loupe who posted a second-round 70 for 137.
Loupe had been among the players who had to return to complete the first round on Friday morning, taking a one-shot lead with a 67.
It was a further two strokes back to Americans Cameron Beckman and Pat Perez on 139. Beckman posted a 70 and Perez a 71.
Bowditch took his late stumble in stride.
"It's going to happen out here," he said, noting that it was balanced out by his eagle.
"My wedge shots have been pretty good," he said. "I was trying to hit it a little past the pin and hope it came back to a reasonable distance and got lucky, it went in."
Bowditch, 30, has made the cut in seven of his 12 US PGA Tour starts this season, a share of 19th place at Pebble Beach is his only top 25 finish of the season.
"My putter has really been a big problem this year," he said. "I'm not making many putts at the moment, so most of my birdies have been sort of coming inside of six or five feet.
"I've hit a lot of good wedge shots. I made a couple of good par saves on my back nine this afternoon, but all in all it's been more of hitting my approach shots pretty close."
Leading scores on Friday in the second round of the $6.2 million (4.5 million euros) US PGA Tour Texas Open (USA unless noted):
136 - Steven Bowditch (AUS) 69-67
137 - Chad Collins 71-66, Andrew Loupe 67-70
139 - Cameron Beckman 69-70, Pat Perez 68-71
140 - Daniel Summerhays 72-68, Kevin Na 70-70, Freddie Jacobson (SWE) 70-70
141 - James Hahn 71-70, Trevor Immelman (RSA) 70-71, Josh Teater 71-70, Will MacKenzie 69-72, Aaron Baddeley (AUS) 70-71, Zach Johnson 70-71, Wes Roach 75-66
142 - Brian Harman 70-72, Jason Kokrak 71-71, Martin Flores 71-71, Jerry Kelly 71-71, Chesson Hadley 69-73, Matt Kuchar 70-72, Fred Funk 70-72, Justin Hicks 69-73, Bo Van Pelt 69-73
143 - Brian Davis (ENG) 71-72, Geoff Og