Another American, Matt Kuchar, shot 71 after four bogeys on the back nine.
The Americans and Denmark were tied for the team lead, three strokes ahead of Portugal. Traditionally a team event, an individual stroke-play competition was added to the tournament this year to mirror the format to be used at the 2016 Olympics in Rio de Janeiro.
Only 12 of the 60 players in the no-cut field broke par.
"I made some good birdie putts today and some par saves as well, so pretty happy," Streelman said. "On 18, the wind tricked us a little bit and it floated me on a hair and it came down in the middle of that bunker and plugged pretty deep. I had no shot. It's going to happen out here, you expect it."
Bjorn had a poor start to his day, four-putting the fourth hole.
"I thought, 'Well, this could be a long day,' but I just kind of kept my composure and made some good birdies and kept playing solid," the Dane said. "It is, in my eyes, probably the finest golf course you can ever play."
Kuchar said he wasn't disappointed with his score. He bogeyed 18, a hole he double-bogeyed at the Australian Masters on Sunday to give Adam Scott as two-stroke win.
"The back side today, certainly 16, 18, are really tough holes," Kuchar said. "I was not able to finish those off as well as I would like to have today, but even par is not a bad score."
Scott, who won the Australian PGA before his Australian Masters victory, had a quintuple-bogey 9 on the 12th hole and shot 75.
Trying to drive over a dog-leg with his tee shot, Scott hit his first ball on the par-4, 440-yard 12th into the bushes in the right rough, then hit a provisional in the same area. He didn't find his first ball and his second was unplayable, so he returned to the tee and hit his fifth shot.
Scott hit through the green on his approach, got on the green for seven and two-putted for nine.
"Just a couple of lazy swings and I paid the price," Scott said. "Just away with the fairies on that hole. When you play good tracks like this you need to be switched on at all times and I paid the price."
The system being used to determine the entries at the World Cup world golf rankings and the number of players eligible from each country based on those rankings will be used at the Rio Games when golf returns to the Olympic program in 2016.