Three days before the FA Cup semi-final against Tottenham, and in the aftermath of Sunday’s pathetic defeat by West Brom, a drama-free win is enough for Manchester United. That is what they achieved thanks to goals by Chris Smalling and Romelu Lukaku. The result tightens their hold on second place in the Premier League and raises spirits, at least a little, before they resume their pursuit of the only trophy they can win this season.

José Mourinho, for one, was encouraged by the improvement he saw from his side, hailing a “good collective performance, with good responsibility and a great attitude”. But he regretted that his players have not always shown those qualities this season. “I spoke with them about that [after the defeat by West Brom],” Mourinho said. “We are inconsistent many times in our attitude. With our top five opponents, we didn’t lose any points. We lost and won against City, Spurs and Chelsea and won and drew against Liverpool. But we lost against Huddersfield and Newcastle. And we lost points against teams that are probably going to get relegated. So I think we were not consistent. And you pay the price.”

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After offering another reminder of his personal roll of honour – “eight titles in four different countries, including three in this country” – he said: “I know why you win and why you don’t win. No doubt about City’s quality and that in any circumstances they would win this title this season but we could have perfectly, I would say, 10 more points this season.”

Mourinho made seven changes to the lineup who were embarrassed by West Brom but perhaps the most intrigue concerned a change the manager did not make: did the inclusion of Paul Pogba, who had been withdrawn before the hour on Sunday, indicate Mourinho wanted to see a performance that would convince him the club’s record signing deserves to start against Spurs?

If so, Mourinho got the display he wanted. Pogba did not cast spells but did play very well. He affected the game positively almost every time he got the ball, which was not often enough for him to be described as having dictated play. Mourinho acclaimed a “top performance” from the Frenchman, who crowned his display by teeing up Lukaku for the goal in the 70th minute that made sure of United’s victory.

Smalling had given United the lead in a low-key first half by converting from close-range after a sharp move. Ander Herrera, the most influential of United’s trio in midfield, was instrumental, playing a neat pass to Jesse Lingard, whose crisp low cross left Smalling with a straightforward finish.

Facebook Twitter Pinterest Chris Smalling converts Jesse Lingard’s low cross to put Manchester United ahead at Bournemouth. Photograph: Mark Enfield/Mercury Press/Rex/Shutterstock

The goal came one minute after Marcus Rashford injected spark into a humdrum game by winning possession off Nathan Aké before firing off a shot that forced a diving save from Asmir Begovic.

Rashford was deployed centrally because Lukaku was on the bench. The 20-year-old looked dangerous, combining well with Lingard and Anthony Martial. All three, without quite catching fire, made reasonable claims for starting at Wembley ahead of Alexis Sánchez.

Other players were given opportunities to stake claims, too – or perhaps just to add another word to their long goodbyes from United. Luke Shaw did fine at left-back on his first appearance since being hauled off at half-time against Brighton last month. The right-back Matteo Darmian did not disappoint on his first league start since October. Marouane Fellaini, who is expected to leave Old Trafford on the expiry of his contract in the summer, completed the midfield trio adequately on his sixth start of the campaign.

United bossed most of the match against hosts minded to make their visit uncomfortable. Josh King did ruffle United just before the break, however, drawing a save from David de Gea with a shot from 20 yards.

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The visitors started the second period as if ordered to wrap up the win as quickly as possible. Bournemouth resolved to try to fend them off and hope to equalise on the break. They came close to doing so in the 56th minute but Callum Wilson was unable to connect with King’s ball across the six-yard box – the striker claimed that was because Shaw had pulled him back but the referee disagreed. Soon afterwards Smalling was booked for dragging down Wilson near halfway. One minute later Steve Cook received a similar punishment for a far more brutal tackle on Pogba. As tempers and the tempo rose a touch, the game became more open. That displeased Mourinho, who decided it was time to introduce Lukaku in an attempt to finish off Bournemouth.

Lukaku soon fulfilled his mission. Racing on to a through-ball from Pogba, he held off Aké and clipped the ball over Begovic into the net from 12 yards.

There might have been a late twist if Wilson had been awarded a penalty after going down in the box following a loose tackle by Smalling but the referee did not whistle and the travelling fans kept singing.