With both teams battling the elements in Wellington, the Springboks had the better of the first half thanks to a Bryan Habana try although three Dan Carter penalties ensured the All Blacks held a 9-8 lead at the interval.
But South Africa failed to score a point in the second half and a converted try from Jerome Kaino proved decisive for the hosts.
So'oialo admitted his team had been hanging on by their finger nails at many stages throughout the match.
"It was a very important win for us," he said. "We were on the back foot throughout the first half but came good thanks to a 15-minute spell in the second.
"South Africa are the best, they're the world champs and have a great defence which we needed to crack.
"I'm just glad the boys came through."
Springboks skipper Victor Matfield is hoping for a turnaround in fortunes when the two teams meet again in Dunedin next weekend.
"We were happy with our first half and feeling confident, but we came out after the break and couldn't hold onto the ball for long enough," said Matfield.
"We need to get rid of the rust but hopefully we'll be better next week.
"It will be a tough week for us but we're proud of what we did and looking forward to playing them again."