Swiss international Schär brought the game to life with an unstoppable effort from range to give the Magpies a 24th-minute lead, one they added to before the break through Longstaff, who produced a composed finish at the Leazes End.
Burnley huffed and puffed in the second half, but – in truth – they rarely looked like breaching United’s well-drilled rearguard, with Rafa Benítez’s side putting further distance between themselves and the Premier League’s drop zone after a second win on Tyneside in four days.
A scrappy opening ten minutes failed to yield a chance at either end of the pitch, though it was United who started to grow into the game first during the following exchanges. Miguel Almirón let fly from the edge of the penalty area after gathering Salomón Rondón’s pass, but his left-footed strike failed to trouble Tom Heaton. Two minutes later, the Burnley ‘keeper was in the right place at the right time to gather Florian Lejeune’s deflected header after the Frenchman got on the end of Longstaff’s cross.
Still, United’s opener – which arrived midway through the first half – came largely out of nowhere. Schär gathered possession from Javier Manquillo and required just a single touch before taking aim with a wonderful, rasping effort from 20 yards which flew beyond Heaton via the woodwork.
Burnley nearly levelled immediately with what was their first meaningful attempt of the game. Jóhann Berg Guðmundsson’s corner from the right was flicked on in the centre and dropped into the path of Chris Wood at the far post, and the New Zealand international brought an instinctive stop out of Martin Dúbravka with a vicious strike.
But, the Clarets soon found themselves trailing further. Almirón set Matt Ritchie away down the left and, despite an awkward touch, the Scot managed to keep the move alive and swing a cross into the middle. Ben Mee did enough to deter Rondón but could only succeed in teeing up Longstaff, who controlled the ball before picking out the far corner.
James Tarkowski ought to have pulled one back for Burnley before the interval, fluffing his lines from deep inside the penalty area after Ashley Barnes’ header looped over the top of the United backline. The England centre half had another sight of goal ten minutes into the second half, heading substitute Robbie Brady’s corner high of the target after rising high.
A brilliant Schär switch paved the way for a United attack with 70 minutes on the clock. Ritchie gathered on the left and delivered a cross for Rondón, whose left-footed effort was blocked by Charlie Taylor. Almirón picked up the loose ball and tried to find the top corner, but the Paraguayan curled off-target.
Clarets manager Sean Dyche introduced towering forward Peter Crouch for the final quarter of an hour, and the 38-year-old immediately put himself about. Burnley’s players looked to find him at just about every opportunity but, when he did win the ball, a member of the United defence was there to sweep up the danger.
Indeed, an 86th-minute goalmouth scramble aside, the Magpies looked comfortable late on. They saw out a hefty chunk of stoppage time before celebrating a second successive 2-0 victory – and a fourth top-flight win on the trot in front of their own supporters.