The overnight leader, who won the 2012 Australasian PGA qualifying school, followed up his opening round 64 with a two-under 70 to join China's Zhang Xin Jun at the top of the leaderboard on 10-under 134.
The 26-year-old Australian dropped two shots at the par-five 15th, the same hole where he had his sole bogey a day earlier.
"That 15th hole, I can't get my head around it actually," Popovic said. "It is really tough judging the wind there, behind the green there is a bunch of trees that are pretty tall.
"I picked the club (nine-iron) straight out of the bag and my caddy and I both agreed on it. I did pull it a bit I admit, but I actually called it to go and it landed over the green and we just sort of looked at each other completely bamboozled.
"Then over the back of the green, I didn't have the best lie... the grass was growing into the ball and then (I) just completely stuffed it up."
Zhang, meanwhile, made the most of his hot putter, sinking seven birdies in his first 15 holes to take sole possession of the lead but two bogeys in the last three holes forced him to settle for a five-under 67 in the tournament.
"I've been surprised by my putting, I needed just 22 putts which is my best-ever putting round, I really like the greens here," Zhang said through an interpreter.
"With my approach shots I'm just trying to visualise them, to think about the shot and hit it, so far it's working."
Former US Open champion Geoff Ogilvy (69) and Matthew Griffin (67) were tied for third, two strokes behind the leaders, while fellow Australians Matt Goggin (66), Steven Bowditch (67) and Brad Kennedy shared fifth spot, a further shot back.
Ogilvy, who started on the 10th hole, hit six birdies but three bogeys cost him the lead at the halfway stage.
"I played quite nicely this morning, I felt like I was a bit loose on the front nine and let a few opportunities go away but I played well on my last nine holes," Ogilvy said. "I'm still in the tournament and that's all you can really ask."