Goals by Marco Reus, Mario Gotze and a Robert Lewandowski brace earned unbeaten Dortmund their third win in five Group D matches and secured top spot in the section with a game to spare. Danny Hoesen netted Ajax's consolation in the closing minutes.
The result sees Dortmund safely into the last 16 alongside second-placed Real Madrid, who drew 1-1 with Manchester City in the night's other Group D encounter and now cannot usurp Dortmund from top spot because of their inferior head-to-head record.
Just eight minutes were on the clock when the visitors went in front, Reus combining well with Gotze down the right before tucking the ball home low beyond Kenneth Vermeer.
Ajax tried to mount a response with Derk Boerrigter seeing a volley blocked away by Lukasz Piszczek and Christian Eriksen curling an effort over the bar from the edge of the area.
But the next goal went the way of the visitors as Dortmund put one foot firmly into the last 16. The home defence appeared to switch off as Mats Hummels' free-kick picked out Gotze who cut inside from the left channel and fired in a shot that beat Vermeer at his near post.
And the contest was as good as over by the interval when Dortmund added a third goal in the 41st minute. Gotze was again involved as his deflected shot drew a good parry from Vermeer, but Lewandowski was the first to react, just beating the despairing Ajax goalkeeper to the loose ball as he fired in the rebound.
Ajax boss Frank de Boer had declared that his side would go "all out to win" the encounter with a talented Dortmund side, but his optimism must have been shattered as his players trudged off at the interval.
De Boer took off Christian Poulsen for Lasse Schone at the break and immediately the hosts appeared to carry more threat as they forced Dortmund goalkeeper Roman Weidenfeller into his first meaningful action after 51 minutes when he parried Eriksen's drive.
Schone drew another save from the opposition goalkeeper as Ajax continued to hunt for a way back into the match, but home hopes were finally extinguished in the 67th minute as Dortmund netted their fourth.
The impressive Gotze added his third assist of the night as he crossed the ball to the back post where Lewandowski controlled the ball smartly before smashing home an impressive finish from a tight angle.
There was still time for another goal before the end as Hoesen curled home a smart finish from the edge of the area, but it was scant consolation on a torrid night for the Eredivisie champions.