The Netherlands boss spoke highly of the Manchester United man, whose double against Romania took him above Johan Cruyff in his country's all-time scoring charts
The former Arsenal man's double, sandwiched between Rafael van der Vaart and Jeremain Lens strikes, took him above Johan Cruyff's tally of 33 goals in an Oranje shirt.
"Van Persie was very unlucky in the first half but in the second half he was actually very happy, because he made an incredible world-class goal," Van Gaal was quoted as saying by Voetbal International.
"It was a ball that he could barely head, but he deliberately hit it into the top corner. And he also put the penalty well inside [the goal].
"He was also a great target man, as you saw in his first goal. And Van der Vaart put his shot in flawlessly. Lens was [also] involved in two goals. And I haven't even talked about the defensive organisation.
"I thought it was the best match [the team has played] in this period under me," the 61-year-old added.
"We were only sloppy in the third quarter, but Romania created only one chance... Beyond that quarter we did what we had agreed [to do]. And behold the result.
"We have taken more steps [forward] and we have to believe in ourselves... We are on our way to our seats for the World Cup in Brazil. But for now we are not there yet," he added.
Netherlands now lie top of qualifying Group D by seven points, with four games left to play.