Depay then hit the Germany crossbar moments before Wijnaldum netted Holland's third goal just before the final whistle.
They face a tough task in their next match on Tuesday, 16 October as they visit world champions and Nations League Group A1 leaders France.
"It would have done our confidence the world of good had we taken those chances but you can see we are lacking confidence after the poor results we've had over the last months, Loew added. Everyone needed this, the players, the staff and the whole of the Netherlands".
Van Dijk reacted first to head in from close range after Ryan Babel had headed against the crossbar following Memphis Depay's right-wing corner.
Substitute Leroy Sane, controversially left out of Germany's World Cup squad and with much to prove in a national team jersey, was played into acres of space in the box but fired wide when he looked certain to score his first worldwide goal.
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Koeman brought on another debutant in Nigerian-born Arnaut Groeneveld, ending the hopes of the African nation that he would turn out for them, as the home side looked to stem a growing German dominance in midfield.
After van Dijk's opener, the Dutch had chances to double their lead but Wijnaldum shot wide and Depay headed off target.
Depay celebrates his goal.
"No one would have believed you if you had said before the game that we would win by a 3-0 scoreline".
"It's hard to answer why we are struggling for goals". The fact is, we had so many chances in the last two games but couldn't score. It was important that we made the 2-0, then it was game over.