Bowditch, buoyed by an early eagle, frittered away a couple of strokes with a double-bogey at his final hole at the TPC San Antonio, but his 67 left him with an eight-under total of 136, one stroke ahead of Americans Chad Collins (66) and Andrew Loupe (70).
The three frontrunners all played in the morning, avoiding a stiff afternoon breeze that sent scores soaring among the late starters.
Phil Mickelson did better than most in the afternoon, shooting 70. He made the cut with nothing to spare after splashing his third shot from the creek adjacent to the green at the par-five 18th to five feet and then holing the birdie putt.
Though the three-time Masters champion will start the third round 11 strokes behind Bowditch, he is delighted at the chance for two more competitive rounds as he tunes up for Augusta in a fortnight.
Bowditch end-of-round lead was his first in 110 starts on the PGA Tour.
"It was nice to get out early before that wind started to get up," the 30-year-old told reporters.
"I'm not making many putts at the moment. Most of my birdies have been coming inside six or five feet. I've hit a lot of good wedge shots.
"I made a couple (of) good par saves on my backside but all in all it's been more hit my approach shots pretty close and get myself in position."
The double-bogey finish came at the par-four ninth, where he fanned his second shot into rough 20 yards right of the hole.
He misjudged his pitch shot and barely got the ball halfway to the cup. His next attempt was not much better, leaving him with a 10-foot bogey putt which he missed.
Despite the poor finish, Bowditch remained positive.
"You're going to have some good shots and you're going to have some bad shots," added the Australian, who has long toiled on the tour but underlined his promise with a tie for second at the Greenbrier Classic last year.
"It's a 72-hole tournament and I just did it on the 36th hole. It's going to happen out there."
It was certainly smoother sailing earlier in the round as he holed out from 82 yards at the par-four 12th.
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- TPC San Antonio