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Lukaku eased the pressure on himself and United with a first half header to help Jose Mourinho’s men bounce back from Sunday’s crushing derby defeat.
But the performance didn’t even come close to making amends for losing to Pep Guardiola’s runaway league leaders.
Lukaku’s second league goal in his last 10 games was the undoubted highlight of an otherwise miserable night in Manchester.
But the Belgium hitman refused to celebrate his winner and if it hadn’t been for David De Gea in the United goal then it could have easily been Bournemouth fans left singing in the rain.
De Gea was the busier keeper and produced a string of impressive saves to frustrate the Cherries.
Jose Mourinho made four changes and recalled forgotten man Luke Shaw, who made his first league appearance since April, as United looked to bounce back.
Manchester United goals and appearances 2017/18
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Phil Jones, Scott McTominay and Juan Mata also returned, while Cherries boss Eddie Howe made four changes himself.
The visitors arrived at Old Trafford in confident mood, having lost just one of their last six outings.
Dan Gosling, Harry Arter, Adam Smith and Callum Wilson came in for Steve Cook, Lewis Cook, Andrew Surman and Jermain Defoe.
But it was United, once again without suspended midfielder Paul Pogba, who started better to dominate possession from the off.
Anthony Martial’s cross just evaded Lukaku and Mata at the far post, but the visitors were also a threat themselves on the break.
De Gea had to get down well to his left to tip wide a skidding drive from Charlie Daniels on 22 minutes before blocking a shot from Dan Gosling.
But moments later Lukaku pounced to head Mata’s cross into the top corner and end the stalemate before a Shaw break and cross almost saw Adam Smith turn the ball into his own net.
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De Gea had to be sharp again before half time to keep out Junior Stanislas’s low drive and an effort from Ryan Fraser as the Cherries continued to attack.
Despite seeing his side fall behind, Howe will have been the happier boss considering De Gea had been the main difference between the two sides.
United were struggling to find top gear as Mourinho stood on the sidelines wondering when his team were going to wake up.
Fraser tried his luck from long range just before the hour mark but there was still no way past the impressive De Gea.
Martial missed an absolute sitter before substitute Marcus Rashford smashed a spectacular effort against the woodwork as United’s frustration continued.
But it still took a fine reaction save from De Gea to deny substitute Jermain Defoe in the closing stages and see United limp over the finish line.