The impact of that loss to leaders City and the ugly scenes that followed it, may hang over United for some time to come although at least their Belgian striker ensured the gap to their neighbours did not grow any greater in the league table.
It was Lukaku’s 14th goal of the season for the Reds, although just his second in his last 10 league games, further fodder for those who accuse him of being a “flat track bully” - prolific against the lesser teams, not so against the better.
Still, last night Mourinho would settle for that and Lukaku struck after 25 minutes, a strange goal and one very much against the run of play after the visitors had enjoyed a strong start to the game.
Anthony Martial shrugged off his marker and slipped a pass to Juan Mata whose superb, hanging cross was the perfect height for Lukaku, up against the much shorter Nathan Ake.
But his header still appeared to lack the power to beat Asmir Begovic, only for the Bournemouth keeper to inexplicably hesitate and watch the ball as it flew into the top corner of his goal.
It was United’s first meaningful attack which, at least, meant Mourinho could congratulate his team on their conversion rate because Bournemouth had just carved out three excellent efforts just before Lukaku’s effort.
On 20 minutes, Callum Wilson’s superb dummy from Ake’s pass played in Josh King whose shot was well blocked by Phil Jones.
Then Charlie Daniels was allowed space to cut through midfield before unleashing a powerful shot that was kept out by David De Gea at full stretch.
Ryan Fraser’s cross just eluded King after 23 minutes but Dan Gosling collected the ball, cut back to a better angle and saw a strong effort parried well by De Gea once more.
As conditions deteriorated in the wind and driving sleet, United bought some breathing space with their goal but Bournemouth were quickly back in their rhythm with a deflected shot from Junior Stanislas drawing yet another fine save from the diving De Gea.
And Francis should have done better when presented with the ball, from a Fraser corner, but skied a shot high over the goal from 15 yards.
That chance had come from an error by Lukaku - as, of course, had City’s winner in Sunday’s Manchester derby - and the Belgian’s mixed fortunes continued before the interval when he was cautioned for a foul on Harry Arter.
Still, Bournemouth were not done and might have been level in first-half injury-time when Fraser’s opportunist near-post crossshot almost caught out the United keeper for once before De Gea made an athletic adjustment to keep it out.
United sought to take better care of the ball after the restart, although De Gea had to pull off a routine stop from Fraser’s long-range shot.
An early shot from Mata, set up by Lukaku’s selfless lay-off, was blocked before Martial missed a glorious chance to double his team’s lead on the hour.
The Frenchman set up Lukaku, whose close-range shot was well saved by Begovic, but when the rebound fell to Martial, in front of an open net six yards from goal, he could only clear the crossbar, under slight pressure from Gosling.
It was a sign of the malaise that has been limiting United on the field in recent weeks, since those halcyon early games of the campaign when Lukaku looked an unstoppable force of nature and United looked capable of challenging for the title.
Mourinho had certainly seen enough and that proved to be Martial’s last significant act, as he made way for substitute Marcus Rashford after 65 minutes.
Rashford’s first touch might have led to a decisive second as he chased Lukaku’s pass into the area and played it back for Jesse Lingard, who summed up United’s display by simply tripping over the ball with a chance beckoning.
At least the introduction of Rashford had brought the desired effect with it. On 72 minutes, he unleashed an incredible strike from 25 yards and wide on the corner of the penalty area which easily beat Begovic but struck the bar and rebounded to safety.
That finally brought Old Trafford to life and Mata quickly followed up with an effort that again required Begovic to save well.
But Bournemouth substitutes Jermain Defoe and Benik Afobe offered more threat after Eddie Howe threw then on and the latter was denied by De Gea’s legs after Adam Smith played him in and deep in injury-time, Fraser drove a shot into De Gea’s body from a Bournemouth free-kick.
De Gea 8; Valencia 7, Smalling 6, Jones 7, Shaw 7 (Young 82); McTominay 6, Matic 6; Mata 7, Lingard 6 (Herrera 71, 6), Martial 5 (Rashford 65, 6); Lukaku 7. Subs (not used) Lindelof, Ibrahimovic, Blind, Romero.
Begovic 5; Smith 6, Francis 8, Ake 6, Daniels 6; Stanislas 7 (Defoe 70, 6), Gosling 6 (L Cook 77, 6), Arter 6, Fraser 9; King 7; Wilson 6 (Afobe 70, 6). Subs (not used) Boruc, S Cook, Surman, Ibe.
G Scott 7