Messi masterclass: Lionel Messi fires brace as Barcelona reach Champions League semis
United started fast and threatened in the opening two minutes through Marcus Rashford, whose shot clipped the top of the crossbar, and through Scott McTominay, who found himself in space in the penalty area only for his touch to let him down.
But United's early pressure nearly turned to despair when the referee pointed to the spot and awarded Barcelona a penalty for Fred's challenge on Ivan Rakitic.
But before the spot-kick could be taken, VAR officials alerted the official to a potential error, and after a review of the decision, the spot-kick verdict was overturned.
But Barcelona didn't have to wait much longer to break the deadlock, as just two minutes later Lionel Messi cut in from the right channel and fired a low effort into the bottom corner with his left foot for his 44th goal in all competitions this season, and his ninth in the UEFA Champions League this season.
The strike also ended Messi's 12-game quarter-final goal drought that stretched back to April 2013.
Before United could recompose themselves, things went from bad to worse as a weakly-hit Messi effort squirmed under the dive of David De Gea to put Barca 2-0 up on the night and 3-0 ahead on aggregate.
De Gea redeemed himself somewhat on the stroke of halftime when he did brilliantly to deny Sergi Roberto, but the United keeper was helpless to stop Barca's third just after the hour mark when Coutinho collected a Messi lay-off and struck a 25-yard rocket into the top corner.
Messi nearly completed his hat-trick with a bicycle kick as Barcelona completely dominated the second half, with their play leaving United chasing shadows.
Jesse Lingard's 79th-minute shot from distance was a rare second-half highlight for United, while the introduction of former Barca star Alexis Sanchez for Lingard a minute later brought a round of applause from the home fans as they recognized the arrival of a former player.
But despite some late pressure from United, the La Liga giants comfortably negotiated the final few minutes without fuss as they closed out a 3-0 win on the night to progress to the semi-finals 4-0 on aggregate.