The Germans, driven by Gotze who had a hand in each of his team's goals, looked capable of scoring every time they broke as they raced to a 3-0 half-time lead against the ineffective four-times former champions.
Marco Reus put the visitors ahead after eight minutes, combining with Gotze in a deadly counter-attack down the right before slipping the ball between goalkeeper Kenneth Vermeer's legs.
With Dortmund needing only a point to go through with a game to spare, Gotze added the second in the 36th minute and Robert Lewandowski scored from a rebound five minutes later after Gotze's initial shot was blocked.
Dortmund coach Jurgen Klopp acknowledged Gotze's important part in proceedings but reckoned the 20-year-old could have done even better.
"Mario played exceptionally but also like we know he can play," Klopp told a news conference.
"But he could have done better in finishing."
"We got a lesson in efficiency from Dortmund but I am also very angry about the way we defended," Ajax coach Frank de Boer told reporters.
