Who needs Cristiano Ronaldo when Marcus Rashford can produce such magic?
Rashford scored a dazzling solo goal, reminiscent of Ronaldo in his pomp, to book United's quarter-final place and take them a step closer to ending their trophy drought.
The Europa League in 2017 was the last time United lifted silverware, under Jose Mourinho, but Erik ten Hag's side remain on course to end that wait after this fine win.
This was United's first game since Ronaldo's acrimonious exit last month, yet there was no sense of missing their former star player, as Rashford's moment of brilliance sealed victory at Old Trafford.
Rashford impressed for England at the World Cup, scoring three goals in Qatar, and continued that form against Burnley with his ninth of the season, just two days after returning to training.
It was a night on which United's World Cup stars shone, with Denmark's Christian Eriksen scoring the opener, set up by Portugal's Bruno Fernandes, with Rashford applying the coup de grace.
United were without skipper Harry Maguire, who had returned to training following his World Cup exploits with England, but he was ruled out of the tie through illness.
Ten Hag included five of United's World Cup stars in his starting line-up – Rashford, Eriksen, Fernandes, Casemiro and Tyrell Malacia, all hungry to put their Qatar disappointment behind them.
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With Maguire absent, Brazil midfielder Casemiro was deployed in central defence and made his experience count, playing with assurance and diligence.
Burnley arrived at Old Trafford three points clear at the top of the Championship, boss Vincent Kompany having lost just two games from 24 since taking over in the summer.
Old Trafford was operating at a reduced capacity of 62,000 because of the strikes by ambulance service workers, with the top tier of the Stretford End closed.
The first chance went the way of the visitors after three minutes, Ashley Barnes flicking a header wide, although he was correctly ruled offside.
Five minutes later, United had their first chance, Taylor Harwood-Bellis ceding possession cheaply, the ball finding its way to Alejandro Garnacho, whose shot was saved by Bailey Peacock-Farrell.
United duly took the lead in the 26th minute with a superbly-worked goal, Fernandes picking out Aaron Wan-Bissaka with an exquisite chipped pass.
Wan-Bissaaka did well to reach the ball and cut it back for Eriksen, who applied a sweeping first-time finish into the roof of the net.
Burnley pushed for an equaliser, winger Manuel Benson cutting in from the right and testing Martin Dubravka with a long-range angled effort, which the United keeper - who looked jittery throughout - palmed away.
United should have doubled their lead six minutes after the restart when Rashford laid the ball off to Scott McTominay, but he skied his effort over the bar and into the Stretford End.
But Rashford made it 2-0 in the 57th minute with his fine solo effort, picking the ball up deep inside his own half and running into the Burnley area before finding the far corner.
Sub Darko Churlinov had a chance to pull a goal back for Burnley, but shot wide of the United goal in the 68th minute.
