The 2010 Open champion shot a three-under 69 to lie one shot behind American Bill Haas. Oosthuizen shares second spot with defending champion Adam Scott of Australia and local favourite Bubba Watson of America.
Oosthuizen, said he was playing good golf.
“I felt like I have been playing well for the last month or so,” said Oosthuizen after his round.
“I have been feeling this coming for a while. I have been swinging well and playing well.”
The Mossel Bay-born player was troubled by a back injury for most of 2013, and it was not 100 percent yet, he revealed.
“I had a bit of a scare yesterday when I picked up my little girl with the back, but I was just glad this morning that it was all good,” said Oosthuizen.
“Some days it is good and some days it is not. It [the injury] is definitely still there. I am managing it pretty good, knowing what I should and should not do.
“One of the things I should probably not do is pick up my little girl running towards me and grabbing her. But it is tough not to do that.”
The 31-year-old Oosthuizen was the best of the six South Africans in the field at Augusta, with 2011 Masters champion Charl Schwartzel on one-over after carding a 73. Ernie Els was two shots behind Schwartzel on 75.
There was disappointment for 2008 champion Trevor Immelman and Tim Clark, who both finished on 79, as well as Branden Grace, who is last in the field on 12-over after ending with an 84.
Zimbabwean Brendon de Jonge, who is playing in his first Masters, compiled a two-over 74.
Oosthuizen said it was an advantage to have finished second at Augusta before.
“It gives you a confidence boost to know that you can do well on the golf course.
“You see it every year with guys that have won here before. If they come in here and they are playing nicely, then they are always up on the leaderboard. I know I can play this golf course. But your game has to be on form.”
The seven-time winner on the European Tour said he was optimistic about his chances over the four days.
“If I am playing well, I can see myself doing really well this week.
“But you know, the few years that I have been coming here, I was just not on my game, I felt like I was struggling with my short game and on these greens, you can’t struggle in that area of your game.
“That’s a huge difference in my game now.”