Headers from Smalling either side of a Danny Ings goal gave the hosts the lead at the break, despite Burnley being well on top for most of the first half, and Robin van Persie’s late penalty secured the victory for Louis van Gaal’s men.
Ings missed two close-range chances and Ashley Barnes fired wide, but the visitors’ challenge faded as the game went on and United continued their fine run of home form.
The result moves United back above Arsenal and Southampton into third place as they made it three Premier League wins in their last four outings.
Burnley gave the hosts an early warning as Michael Keane headed a glorious chance wide from a corner, before Van Gaal’s men opened the scoring from a set piece of their own.
Seconds after Phil Jones limped off and Smalling replaced him, the defender rose high to meet Radamel Falcao’s header back across the box from a United corner, and he nodded into the net to put the hosts in front inside six minutes.
Their lead didn’t last long, though, as red-hot striker Ings levelled things six minutes later, meeting Kieran Trippier’s superb ball in from the right to power a diving header past David de Gea and into the top corner.
Sean Dyche’s men had United rattled and continued to press and harry their opponents, causing all sorts of problems in the hosts’ half. An Ings volley was parried away before Barnes went close as he fired a first-time shot just wide of De Gea’s post.
But it was Van Gaal’s side who led at the break as Smalling grabbed his second three minutes into first-half stoppage time, meeting Angel Di Maria’s cross at the far post and nodding into the net past a helpless Tom Heaton.
Ings had a chance to level things shortly after the break as his flick for George Boyd set the visitors away. Boyd’s cross from the right was missed by two defenders, but Ings could only hit his shot straight at the goalkeeper.
Neither side could make much of an impact as the game wore on, but the killer blow came on 82 minutes as Di Maria raced into the box and Scott Arfield brought him down. The referee pointed to the spot to award United their first penalty of the season, which Van Persie hammered into the corner of the net.
Di Maria then hit a shot straight at Heaton before Adnan Januzaj saw his low shot cleared off the line with the goalkeeper beaten, but it wouldn’t matter as the hosts completed their victory to go back up into third place.
Charlie Nicholas’ verdict
“Not a great performance, but all of a sudden they’re third. How does that happen? I still don’t think they’re good enough. If they keep playing like this I don’t see how they can make the top four.
“They were awful defensively, and going forward Falcao was sluggish and Rooney’s too deep for me. I know they keep winning and they’re in the top four – as long as that happens, they don’t really care.”
Manchester United: De Gea (7), McNair (6), Jones (5), Evans (5), Rojo (6), Blind (6), Di Maria (7), Rooney (6), Januzaj (7), Van Persie (6), Falcao (5).
Used subs: Smalling (8), Herrera (6), Wilson (6).
Burnley: Heaton (7), Trippier (7), Keane (7), Shackell (6), Mee (6), Boyd (6), Arfield (5), Jones (5), Kightly (7), Barnes (6), Ings (8).
Used subs: Vokes (6), Jutkiewicz (6).
Man of the match: Chris Smalling
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