Friday's International Champions Cup clash was the first real test of the Portuguese's reign following last weekend's straightforward win at Championship new boys Wigan.
United had a much tougher workout at a half-empty Shanghai Stadium as Thomas Tuchel's Dortmund deservedly triumphed 4-1, with Henrikh Mkhitaryan scoring a consolation goal against the club he left just weeks earlier.
Mourinho named a strong-looking side for the first match of the Reds' short tour of China but they created little in the opening period, with Gonzalo Castro giving the Bundesliga side a 19th-minute lead.
Dortmund went further ahead as Pierre-Emerick Aubameyang fired home from the spot after stand-in United captain Antonio Valencia handled, before the impressive Ousmane Dembele rifled home after skipping past half-time introduction Marcos Rojo.
Mkhitaryan pulled one back from a Juan Mata pass but United were unable to muster another, with Castro's fine late strike adding extra gloss to Dortmund's win on an energy-sapping night.
United's tour continues onto Beijing as they take on Pep Guardiola's City in the first Manchester derby to be held on foreign soil, assuming storms do not force off the Bird's Nest meeting.
Weather was always likely to be testing in China and in sweltering Shanghai the players trudged out in 32 degrees Celsius and 75 per cent humidity.
It was little surprise that play started slowly and it rarely sped up from United's perspective, with any quick passing let down by poor decision-making.
Memphis Depay, deployed at centre-forward, struggled to get going and saw an attempted cross easily blocked as decent build-up play failed to lead to a clear-cut opportunity by the time Dortmund took the lead.
Aubameyang's long-range free-kick proved difficult for Sam Johnstone and though the third-choice goalkeeper did well to prevent Dembele's follow-up, the ball fell for Castro to fire home.
Jesse Lingard snatched at a chance to level soon after and, having enjoyed a much-needed drinks break, Dortmund pulled further ahead.
Valencia was adjudged to have handled Aubameyang's acrobatic effort and referee Wang Di pointed to the spot, with the striker coolly slotting down the middle
Aubameyang threatened to increase the deficit before half-time, hitting wide and then catching Phil Jones out to get away a shot that Johnstone impressively scrambled away.
England forward Marcus Rashford was among four alterations as the teams emerged for the second half, which was just 12 minutes old when Dortmund pulled further ahead.
Rojo, one of the half-time changes, was all too easily beaten by Dembele and punished as the highly-rated teenager rifled into the top right-hand corner.
Mkhitaryan, denied before Dortmund's third by Roman Weidenfeller, gave the local United fans something to cheer in the 59th minute by simply turning home a Mata lay-off, but that that was as good as it got.
Marc Bartra tried an audacious flick and Nuri Sahan threatened when the Germans returned to the attack, with Christian Pulisic firing just wide from distance as the match came to a close.
There was still time for Dortmund's fourth as Castro scored the goal of the night, hitting a fizzing strike across Sergio Romero into the top corner.
Source : PA
Source: PA