Dortmund, who were competing in their fifth pre-season affair compared to United's second, made their extra sharpness count as they raced into a two-goal lead in the first half in Shanghai.
Gonzalo Castro stabbed home a scrappy opener and Pierre-Emerick Aubameyang scored a penalty after Antonio Valencia handled inside the box, before new boy Ousmane Dembele scored a fine solo effort to stretch the lead after the break.
Henrikh Mkhitaryan, who joined United from Dortmund earlier this month, scored his first goal for the club to reduce the arrears, but Castro's classy long-range finish restored his side’s three-goal cushion.
United, who were only competing in their second friendly, lacked a sharpness in the final third that should improve as Mkhitaryan gets more game time, while Wayne Rooney and new arrival Zlatan Ibrahimovic are yet to play in pre-season.
Meanwhile, Tuchel can take plenty of encouragement from Dortmund's performance and he still has Mario Gotze - who re-signed from Bayern Munich this week - and Andre Schurrle to integrate into the team.
The opening exchanges had all the hallmarks of a friendly encounter with little action of note, before Dortmund opened the scoring in scruffy circumstances.
Sam Johnstone failed to adequately deal with Aubameyang's tame free-kick and, although the goalkeeper saved Dembele's follow-up, Castro scooped home the rebound.
Jesse Lingard fluffed a one-on-one as United sought a quick response, and Dortmund went 2-0 in front when Aubameyang sent Johnstone the wrong way from 12 yards after Valencia was penalised for handball in the area.
Johnstone prevented a deft chip from Aubameyang shortly before the break, but it was 3-0 in the 57th minute when Dembele finished a fine run by leaving Marcos Rojo flat on his back and lashing into the right-hand corner from the edge of the box.
United pulled a goal back when half-time substitute Marcus Rashford cleverly dummied for Juan Mata, who laid on for Mkhitaryan to tap in.
Mourinho did raise a cheer from the crowd with a classy backheel when retrieving the ball, but it was Dortmund celebrating again four minutes from time when Castro fired a 25-yard effort into the top left-hand corner to round off the win.
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