Strengthening the heart of his defence was Mourinho’s priority and it showed as Victor Lindelof and Eric Bailly endured a torrid afternoon on England’s south coast.
In a tempestuous pre-season, Mourinho also clashed with Anthony Martial when the Frenchman failed to return to the club’s pre-season tour of the United States after the birth of his second child.
But Martial was recalled to the starting line-up in the absence of the injured Alexis Sanchez and had the first chance when he dashed inside two Brighton defenders before seeing his shot blocked by Duffy.
The story could have been very different for the visitors had Lukaku not wasted a huge chance to open the scoring when he pulled his shot wide of the near post 10 minutes in.
Instead, Brighton went in front when veteran striker Murray caught Lindelof ball watching to flick home Solly March’s cross with a classy finish.
Two minutes later, the hosts led 2-0 as Duffy was given the space to control and fire past a helpless David de Gea after United failed to clear a corner.
Despite suggesting he is unhappy at Old Trafford after scoring in last weekend’s 2-1 win over Leicester, Paul Pogba was again handed the captain’s armband by Mourinho.
However, there was little sign of Pogba leading United out of the mire as he and summer signing Fred, who cost a reported 52.5 million euros (57.9 million euros, $66.3 million) struggled to control the game in midfield.
Brighton’s failure to defend set-pieces cost them in a 2-0 defeat to Watford last weekend and threatened to undo their good work again when Lukaku was left unmarked just five yards out to nod home Luke Shaw’s deflected cross and give United a lifeline.
That reprieve lasted just 10 minutes, however, before more rash defending by Bailly allowed Brighton to restore their two-goal lead.
Dale Stephens beat Fred to a loose ball in midfield and released Gross before the German was brought down by a lunge inside the area by the Ivorian.
De Gea got a touch to Gross’s penalty but couldn’t keep it out to compound a miserable first 45 minutes for United.
Mourinho turned to two of England’s World Cup heroes in Marcus Rashford and Jesse Lingard at the break in search of inspiration.
But the damage had already been done as Brighton sat comfortably on their lead until virtually the last kick of the match.
Pogba reduced United’s deficit by blasting home from the spot after Duffy felled Marouane Fellaini, but it was too little, too late.
Mourinho’s third seasons in charge during his second spell at Chelsea and at Real Madrid never recovered from a poor start.
His time at Old Trafford threatens to go the same way, particularly with Tottenham next up a week on Monday.