Soothing words pivotal for Parker confidence
Parker's goals, which kept alive his team's chances of reaching the semi-finals, came just three days after he cost his team victory against Iraq by getting in the way of a team mate's shot.
"My team mates supported me after what happened on Sunday," Parker told a news conference. "After the game they told me to put it behind me, that it was part of football.
"When the coach announced the starting lineup for the New Zealand game and I saw that he had put me in, I got my confidence back. I saw he had confidence in me and I was able to put it behind me."
Parker's two goals were all South Africa had to show for a dominant performance.
"We could have had two or three more goals," said coach Joel Santana. "I was satisfied with the victory, the way we moved the ball around and the number of opportunities created."
South Africa now face European champions Spain in their last Group A game on Saturday.
"We are going to try and play that game as equals," the Santana said.