Oosthuizen, who won the Open in 2010, topped the leaderboard with four holes to go, but then played a disastrous 15th hole, finally putting in for a triple-bogey eight which took him to one-under.
A bogey on the 18th saw him sign off on a three-over 75 to lie on even-par.
He said he simply could not explain what went wrong. “I’m still trying to figure out how that four-iron went that far. I took more club obviously with that pin but my play was always pitching it five yards from the back.
“For some reason I pitched it way, way too long and it went through into the rough. I then got myself in a really awkward spot and did not have much option but to go for that chip.
“If I had gone left, I would have ended up in that bunker and that was even a more difficult shot. On this golf course, it’s all about leaving yourself in the right spot and I will know now not to go there again.”
He drew some consolation that the triple bogey had happened in the second round. “There is still a lot of golf to be played. At the moment, I’m five off the pace and 36 [holes] to go, so I’m happy.
Oosthuizen will go into Saturday’s third round seven behind overnight leader Bubba Watson. The 2012 Masters champion started a five-birdie run on the 12th hole and, even though he dropped a shot on the 18th, the American has a three-shot lead over Australian John Senden. Fellow Australian and defending champion Adam Scott, local favourite Jordan Spieth, Dane Thomas Bjorn and Swede Jonas Blixt are tied in third place on three-under.
The 31-year-old Oosthuizen said he believed he could still play himself into contention. “I think it’s more frustrating, disappointing, when you have nine holes to play on Sunday and something like that happens. At the moment I’m still in a good position for the tournament.”
2011 Masters champion Charl Schwartzel and four-time Major winner Ernie Els missed the cut by a shot. Els, who started on three-over, added a round of 74 to lie five-over for the tournament, while Schwartzel had a disappointing round of four-over to also finish on one-over.
Branden Grace was the only South African to break par on the day, but his 69 was too little, too late after he had played a disappointing 84 in Thursday’s opening round.
Grace said his two rounds were as different as day and night. “Everything was different. Yesterday [Thursday] I played a little bit protective golf, and today [Friday] I knew I had to shoot a number. That’s what I tried to do.
“I was really good from tee to green today and that was the big difference.
“This golf course gets to you, and if things go wrong out there, they go wrong properly. That is the thing about Augusta. You miss a couple of greens at the wrong spots and you walk away with the numbers. … But it was just nice knowing that I can go away, leaving Augusta on a positive note.”
Tim Clark played two double-bogeys in his round of six-over 78 to finish on 13-over for the tournament, while Trevor Immelman, who won at Augusta National in 2008, carded a two-over 74 and finished the tournament on nine-over.
The other southern African in the field, Brendon De Jonge of Zimbabwe, made the cut after scoring an even-par 72, having finished with a two-over in Thursday’s opening round.
The third round will be played on Saturday, with the final round scheduled for Sunday.