Popovic, who nearly gave up golf earlier this year to care for his ill father, followed his opening-round 64 with a 2-under 70, including a double-bogey 7 on the par-5 15th.
The tour rookie is tied with Zhang Xinjun (67) at 10 under, two shots clear of the field at the Palmer Coolum resort course.
Zhang had a one-stroke lead twice in the closing holes, but bogeys on two of his final three holes dropped him into a tie with Popovic going into the weekend.
Last week's Australian Open champion, Peter Senior, shot a 70 and was tied for eighth, four strokes behind the leaders. Former British Open champion Darren Clarke had a 69 and was another stroke back, while South African Rory Sabbatini shot 68 after an opening 76 to make the cut with a few strokes to spare.
Ogilvy, the 2006 U.S. Open winner, is aiming to finish in the top 50 in the year-end world rankings, which would guarantee him a spot in next year's Masters. Current projections show Ogilvy would have to finish third or better at Coolum.
"I don't know if it has to be first to get into the top 50, but it probably has to be first two or three," Ogilvy said. "I don't study world rankings that much. But that would be a bonus; winning the tournament would be the best part, but if that was a side bonus, that would be good.
"I feel like I am in a good place. It's nice I will be in one of the last few groups tomorrow, and if I can have a good score, maybe get right up there after tomorrow and give it a crack on Sunday."
Popovic found out earlier this year that his father, Radi, is suffering from a form of incurable bone cancer. The Australasian PGA Tour rookie said his father, in the hospital undergoing blood tests, was in tears after his opening round, and expected more of the same Friday.
He misjudged the wind on 15, leading to the double bogey.
"Then we didn't have the best lie, there was a lot of into the grain, the grass growing into the ball and then I just completely stuffed it up," he said.
Zhang, who needed only 22 putts Friday and has preferred his hybrid club to his driver off the tee on all but three occasions for two rounds, said through a translator that he's becoming more confident as he plays the course more. Last year, he watched the PGA at Coolum on television from China.
"I felt good today; I am getting used to this layout and to the wind," Zhang said.
Asked how he communicates with his non-Mandarin speaking Australian caddie Drew Garland, who was provided by the tournament office, Zhang said: "I've learned some English, mostly related to golf, like, 'How do you think this breaks?'"
Bowditch grew up in the area, and his family still lives at nearby Peregian Beach. He said he has taken plenty of confidence from securing his PGA Tour card for next year at the recent qualifying school in California.
"Q-school is one of the most demanding golf events I have ever had to play," Bowditch said.