The visitors were ruthless against Ajax, scoring three times in a superbly efficient first half for their biggest ever win in the competition to secure top spot in Group D ahead of nine-times European champions Real Madrid with a game to spare.
In a group that also contains big-spending Manchester City, the German champions have enjoyed a far more assured run in their second successive Champions League campaign after faltering at the group stage last season.
"To win the group with a game to spare is something that none of us believed would happen when we saw the draw," said Dortmund coach Juergen Klopp, who has also led his team to back-to-back Bundesliga titles over the past two seasons.
"It is crazy but it is something the team has earned. We will continue in the Champions League in the next year and that is unusual," he said of Dortmund's first venture into the knockout stage since 2003.
"This match was another milestone in the club's unbelievable history. I am proud of my team."
Madrid and Manchester City both needed late home equalisers to spare their blushes against a lightning-quick Dortmund attack with Mario Gotze, Marco Reus and Robert Lewandowski showing no fear against their more illustrious opponents.
The trio combined again on Wednesday, taking the four-time European champions apart with Gotze and Reus, who scored after a stunning 80-metre run, on target once. Lewandowski added two more for an eye-popping 4-0 lead before Ajax pulled one back.
"If they keep playing like that then it does not matter who they will play in the next round," honorary Bayern Munich president Franz Beckenbauer remarked.
"If you play Real Madrid twice the way they have done in this group, then a Champions League victory is possible for them."
Dortmund beat Real 2-1 in Germany and drew 2-2 in Madrid with the hosts rescued by an 89th-minute equaliser.
Bayern have felt the Dortmund fury first hand having failed to beat them in the past two years as the 1997 Champions League winners challenged the Bavarians' long-standing domestic dominance.
"We would have never believed such a run before the start of the season," said 20-year-old German international Gotze, who had a hand in all of his team's goals on Wednesday and has quickly risen to become one of Europe's most-coveted players.
"We really wanted the last 16 spot and we did it. We can be happy both about the game we played as for the result. We are looking forward to the next games," he added.
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