Branden Grace was once again the South African side's top finisher, with 11-under in T5, while Oosthuizen finished two shots back in T12 (-9), Burmester T15 (-8) and Charl Schwartzel T39 (+2).
The skipper was proud of the effort that saw the team finish on the podium for a second successive event, after ending second on home soil last month.
"Ja, I played nicely, made a bit of a scare there on the 18th hole but ended up making a good bogey, but I felt really comfortable and hit the ball pretty well," said Oosthuizen.
"It was tight, we were tied with Torque with, I think, three holes left and I think Carlos Ortiz didn't finish well and I added a birdie also so we hung onto third place, which is good for the team."
Individually, Schwartzel in particular struggled in the first two rounds and Oosthuizen defended the former Masters winner following his appearance at Augusta the week prior.
"A lot of confidence, I feel like my game is slowly getting there. In the team, I think a two week break is good for Charl, he's played a lot of golf – I think seven [events] in nine weeks or something, so I think two weeks will do him very good," he pointed out.
"You can see the guy is just a little bit fatigued and I think for Virginia we'll be nice and fresh, and obviously Branden is playing some good golf, and Dean is very close to being very good again, so we're all looking forward to the next one."
Legion XIII captain Jon Rahm was the individual winner, finishing an impressive six shots clear at 21-under par, while his team also claimed the win with a massive nine-shot advantage at 45-under par.