Gonzalo Castro scored the opening goal for Dortmund and Pierre-Emerick Aubameyang increased the lead from the penalty spot.
In the second half, young midfielder Ousmane Dembele scored the third goal which crushed United's condfidense.
Henrikh Mkhitaryan scored a consolation goal for the English giants, but Castro completed a brace with a long range strike in the ending minutes of the match.
Even though, United suffered a crushing defeat, their manager Jose Mourinho refused to panic. The Portguese manager termed it as just a friendly game and they would learn from the mistakes.
Addressing the media, the manager said: "Unfair to make any decision. Day by day they are starting to win my trust.
"I know in pre-season the team in the advanced stage of preparation looks better," he said.
"It happens year after year. It was too obvious. We knew after 10 minutes that one team started training a month ago and played four games.
"The reality is even in this situation we have six players still in Europe, plus (Wayne) Rooney and (Chris) Smalling who are only training. That is eight not involved.
"We had no (Zlatan) Ibrahimovic, (Anthony) Martial, (Marouane) Fellaini, (Morgan) Schneiderlin - lots of them aren't here yet."
Jose further stated that he needs one more signing to bring a balance in the squad. Manchester United have already signed defender Eric Bailly, midfielder Henrikh Mkhitaryan and star striker Zlatan Ibrahimovic.
Mourinho was quoted: "Our fundamental market is 75 per cent done and when we sign one midfield player, that will be done.
"The fundamental market is four players and we just need that crucial one."
Manchester United are closing in on signing Paul Pogba from Juventus this summer. The Red Devils are about to break transfer records as they are ready to place a world record €125 million.