Forward Mario Gomez struck twice to sink the Dutch, adding to his goal in the opening 1-0 win over Portugal, as Germany made it two wins from two.
"We really wanted today to take that second step," said Low.
"It was important to keep at it in the second game and the door to the quarter-finals has now been opened. I believe it will be very important [to beat Denmark in their final game]. It would be good not to have to travel for the last eight [and play in Gdansk]."
Germany will qualify as group winners if they draw or win their final match in Lviv on Sunday.
They could still qualify if they lose that match and would also advance if Portugal, on three points after beating Denmark 3-2 earlier on Wednesday, fail to beat the Netherlands, who have only an outside chance of remaining in the tournament after two defeats.
Low praised both Gomez and midfielder Bastian Schweinsteiger, who created both Germany goals and is hitting top form after suffering a thigh injury in May.
"The goals were great by Gomez. He's got good self confidence from the whole season and it's good for him," Low said.
Turning to Schweinsteiger, Low added: "He is getting better and better, he's developing more of a presence and when it gets tough he can keep the ball. He's physically strong and wins a one-on-one."
Gomez said Germany should not get carried away with their impressive start as the seek to win a first major trophy since 1996.
"Expectations are great, we got off to a good start but there is a long way to go," he said.
