A second half own goal by Daniel Agger and a late Dirk Kuyt effort were enough for the highly-fancied Dutch, but it was not all plain sailing in Johannesburg.
They struggled to create openings in the first period, before the goal came from an unlikely source to break the Danish resistance.
They eventually held on for a good start to Group E, which also includes Japan and Cameroon, and for their coach it was just reward after years of planning.
"I've been thinking about this first game for a long, long time," he said. "I've always said that this was the most important match because a good beginning to a world championship is so important.
"It's always a tough match. Today, as you could see, there was a bit of tension with the players. It was difficult, but we won, which is the most important thing."
Van Marwijk, whose side always flatter to deceive at major global events, struggled through the first 45 minutes and looked short of ideas without the injured Arjen Robben. But they looked a changed team after the break.
The coach said: "Beforehand, I think we were the favourites, so you know you're going to face a very defensive opponent.
"That means that in your build-up, you cannot afford to make many mistakes. But we played well, we didn't give away too many opportunities and all the players should be complimented for that.
"I think we made a reasonably good impression and that we never panicked, not for one moment. In the end, we are really pleased with this win."
Opposite number Morten Olsen paid tribute to the Dutch, but admitted that things could have been different had they not conceded a goal so early on in the second half. He said: "It was a deserved victory, I think. The Dutch team is perhaps not the favourite, but certainly an outsider to win the World Cup.
"It could have been different if we didn't have the thing that happened a few seconds into the second half, but that's the kind of thing that decides football matches - the first goal and we know that. Obviously now the Dutch were in the position they really liked. They would have enjoyed the second half much more, that's for sure."
But he paid tribute to his team, saying: "What I would like to say about my own team is that they put in a good effort. We were well positioned in the pitch during the first half, not so much in the second half."
Olsen also shed light on his decision to field Nicklas Bendtner, less than 24 hours after insisting the Arsenal striker "cannot play" due to injury.
He added: "We had to take some chances in this match and I was not bluffing when I said Nicklas Bendtner was not going to play. He wasn't going to play. Then yesterday we had new injuries from Jon Dahl Tomasson and Daniel Jensen. We didn't have the same number of offensive players, so we had to take the risk."