The game, played in warm weather under clear blue skies and ended in a 2-0 win for the Dutch, was a slow, stop-start spectacle for more than 83,000 fans in the stadium which is hosting eight matches in the tournament including the final on July 11.
The match was the third at high altitude in Johannesburg but the players of South Africa and Mexico who drew 1-1 in the tournament's opener on Friday made no reference to it as they were more used to the conditions.
The high altitude of Argentina's match against Nigeria at Ellis Park in Johannesburg on Saturday did not seem to bother those players either.
However the first match between two European teams, and those from low-lying countries at that, did have an effect, according to Dutch forward Dirk Kuyt who scored his team's second goal five minutes from time.
"Both teams had to adjust to the higher altitude which was different," Kuyt told reporters when asked to explain why the first half especially was so poor.
He agreed the match was not a great spectacle for the fans, adding "that had everything to do with the altitude."
"The first half was very tough, I felt strange and had a dry mouth all the time - but it improved after the break," Van Bronckhorst told Reuters.
"I'm exhausted," he said. "I thought we played really well in the first half, but in the second half, after they scored, they could relax, play with the ball on the ground, and we had to do all the running."
"You feel you are breathing a bit heavier," he said. "But the main difference for me is that the ball comes out quicker.
"It's harder to control, but that's what the teams have to deal with, and whoever deals with it the best may get to the final.
"Most of the games are played up here, so you're not going to win if you can't deal with it. The ball is tricky and not just for the keepers but for all the players."
