Temperatures of 35 Celsius (95 Farenheit) at the 8:00 pm kick-off time in Shanghai meant the International Champions Cup match was largely played at a pedestrian pace with frequent breaks to take on water.
Mourinho did not include Wayne Rooney, opting to give his captain more time to get fit after only joining the squad earlier in the week after Euro 2016.
Dortmund enjoyed the better of the early skirmishes and when they took the lead in the 19th minute the United defence had only themselves to blame.
A long-range Pierre-Emerick Aubameyang free-kick was parried by inexperienced 23-year-old goalkeeper Sam Johnstone as it dipped in front of him.
The reserve gloveman was forced into a quick double save by Ousmane Dembele’s follow-up but Gonzalo Castro scrambled home at the third attempt from six yards.
United’s woe deepened when Aubameyang, who bagged 25 goals in 46 matches last season, doubled Dortmund’s advantage from the penalty spot in the 35th minute after Antonio Valencia handled Castro’s cross.
Dortmund, playing the fifth match of their pre-season campaign, were much sharper than United who had just the single outing against Wigan before boarding the plane to China.
“I think after 10 minutes you could tell who started training one match and 10 days ago and who has had one month and four games,” Mourinho told reporters after the match.
“This was Formula One against Formula Three, they are much sharper.”
United’s only chance of the first half fell to Jesse Lingard on the break, but his weak right-foot effort was easily snaffled by goalkeeper Roman Wiedenfeller.
The second-half exploded into life in the 57th minute.
Frenchman Dembele scored the goal of the night as the summer signing from Rennes turned Marcos Rojo inside-out before burying a right-foot shot into the corner for Dortmund’s third.
Two minutes later new midfielder signing Henrikh Mkhitaryan scored his first goal for United — against his old employers — when he slotted into an empty net after being set up unselfishly by Juan Mata.
Mkhitaryan, who could have scored a couple more, shone brightest for Mourinho’s undercooked side as the North Rhine-Westphalian giants sealed an emphatic win in spectacular style when Castro smashed home a stunner four minutes from time.
“It’s been 10 days of work. People are really tired,” said Mourinho. “High quality opposition and the reality is we have six players still in Europe plus Rooney and (Chris Smalling) who are only training.
“That is eight not involved. Some others are not going to stay in the squad and it will be different than it is at the moment.”
United wrap up their tour against Manchester City in Beijing on Monday.