The creative attacker was in fine form as he led the Bundesliga representatives to a deserved away win against the Godenzonen
BVB needed only eight minutes to open the scoring via Marco Reus, before Mario Gotze doubled the lead with a fine finish. A somewhat fortunate Robert Lewandowski strike then put the match to bed shortly before the interval, with Lewandowski making it four after the break. Substitute Danny Hoesen pegged one back for the hosts in the closing stages of the game.
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, and calmly slotted home after receiving the ball back.
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 jinking 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 and came close in the 51st minute. Eriksen beat the offside trap after 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 Amsterdam side would eventually get a goal. 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.
Ajax remains Group D's number three with four points from five games. It travels to Real Madrid on Dec. 4 in its last Champions League game of the season.
Dortmund sits first in their section with 11 points, and hosts Manchester City on Matchday 6.