The creative attacker was in fine form in Amsterdam, racking up a goal and two assists as Jurgen Klopp's men clinched top spot in their pool
BVB needed only eight minutes to open the scoring via Marco Reus, before Mario Gotze doubled their lead with a fine finish.
A somewhat fortunate Robert Lewandowski strike then put the match to bed shortly before the interval, and the Polish striker made it four after the break. Substitute Danny Hoesen pegged one back for the hosts in the closing stages of the game but the game had long since ended as a contest.
The Bundesliga champions started the match the better side of the two, and grabbed the lead in the eighth minute. Reus set up Gotze down the right, then continued his run into the Ajax area before calmly slotting home after getting the ball back from his team-mate.
Ajax immediately tried to hit back and threatened through both Derk Boerrigter and Christian Eriksen after a corner. Nevertheless, the former's shot was blocked by the Dortmund defence, while the latter placed his attempt high and wide.
Sloppy defending after a BVB free kick in midfield resulted in the guests' second goal of the evening. Gotze was left unmarked after Mats Hummels' pass from midfield, and cut inside from the left before jinxing past Ricardo van Rhijn and beating Kenneth Vermeer with a low shot at the near post.
Things would only get worse for Ajax in the remainder of the first half. Gotze tried his luck with a volley from outside the area in the 41st minute, after Daley Blind's poor clearance, only to see his deflected shot parried away by Vermeer. Lewandowski was quick to pounce on the rebound, though, and tapped home from close range.
Ajax started the second half with attacking intention as they went looking for a consolation goal and they came close in the 51st minute. Eriksen beat the offside-trap to latch onto a pass from Boerrigter, but good positioning from Roman Weidenfeller prevented the 3-1.
Dortmund once more proved to be much more clinical in front of the goal in the 67th minute. Gotze sent in a delightful cross for Lewandowski, who superbly controlled the ball before firing home from a narrow angle.
The home side kept on trying to unlock the Dortmund defence and came close to making it 4-1 after 78 minutes of play. Blind curled in a low cross for substitute Viktor Fischer, who did not hesitate, before unleashing a good shot from inside the area only to see Weidenfeller push it wide.
The Amsterdam side would eventually get the goal they deserved, though. Eriksen set up Hoesen after a fine piece of skill and the former Fulham youngster found the net with a deflected shot off Neven Subotic.
It offered scant consolation for an Ajax side who need to beat Real Madrid at the Santiago Bernabeu on matchday 6 if they are to claim Europa League football. However, they will finish third if Borussia Dortmund, who will progress to the last 16 as group winners, even draw with Manchester City in their final fixture.