With a 1-0 advantage from the first meeting at Old Trafford, the Catalans took command inside the first 20 minutes thanks to a double from their number 10, the second of which owed plenty to a dreadful mistake from David de Gea.
Ole Gunnar Solskjaer named an attacking line-up featuring Anthony Martial, Jesse Lingard and Marcus Rashford, but the blow of those first-half goals seemed to drain any hope of repeating the kind of performance they produced to stun Paris Saint-Germain in France in the last 16.
Rashford prodded a shot against the bar in a positive start from United, but they engineered their own downfall within the space of four minutes.
Ashley Young dithered in possession and lost the ball near his own box, allowing Messi to step into space and drill a shot beyond De Gea and into the bottom-left corner.
The United keeper could do little about it, but he endured a calamitous moment 20 minutes in, allowing Messi's tame right-foot shot to squeeze beneath his body and into the net.
De Gea denied a certain Sergi Roberto goal after Messi left Phil Jones chasing shadows, but he was again helpless as Barca struck a third on the hour mark, Coutinho sending a stunning strike beyond his outstretched right hand.
Marc-Andre ter Stegen made a magnificent 90th-minute save from substitute Alexis Sanchez, but United were well beaten and must now fight to turn around their recent form after a fifth defeat in seven games in all competitions.
24 - Barcelona’s Lionel Messi has scored 24 goals in 32 Champions League games against English opponents, more than any other player in the competition. Unstoppable. #FCBMUN pic.twitter.com/laLDNO6gFa— OptaJoe (@OptaJoe) April 16, 2019
What does it mean? Messi just warming up as United's season falls apart
The optimism Solskjaer brought back to United appears to have run dry. They started positively but gifted Barca the tie with mistakes, making it eight years now without a semi-final appearance. A return to next year's competition is no guarantee, either.
As for Barca, they might have looked short of their best at times across the two legs, but Messi looks like a man on a mission this season. With him in such form, a treble is very much on the cards.
Messi the master of ceremonies
The entire game seemed to dance to Messi's tune. His second goal - his 45th of the season - might have been fortunate, but he deserves all the plaudits that come his way. He appears determined to get his hands on this trophy again.
De Gea is becoming a problem
There is simply no reason a goalkeeper of De Gea's calibre should have allowed Messi's second to go in. Solskjaer denied a recent suggestion from Gary Neville that De Gea has perhaps become distracted by ongoing contract talks, but the continued errors in his performances are difficult to ignore.
3 - David de Gea has made three errors leading to opposition goals in all competitions this season - the only Premier League goalkeepers to have made more across all competitions in 2018-19 at club level are Asmir Begovic (5) and Jordan Pickford (4). Agonising. #FCBMUN pic.twitter.com/opnQREo1qK— OptaJoe (@OptaJoe) April 16, 2019
Key Opta Facts
- Barcelona have qualified for the Champions League semi-finals for the first time since the 2014-15 campaign under Luis Enrique.
- United have now been eliminated at the quarter-final stage on seven occasions – more than any other side.
- Messi scored his first Champions League quarter-final goals since April 2013, ending a run of 12 matches and 50 shots without a goal in last-eight matches.
- This was United's heaviest aggregate defeat (0-4) in a two-legged European tie; their previous heaviest was 2-5 vs Milan in the 1957-58 European Cup semi-final and 1-4 vs Atletico Madrid in the last 16 of the 1991-92 Cup Winners' Cup.
- United have lost four consecutive away matches in all competitions for the first time since October 1999 – current manager Solskjær featured in all four of those 1999 defeats.
- Messi has scored 45 goals in all competitions for Barcelona this season – 10 more than any other player in the top five European leagues.
- Spanish teams have lost just one of their last 24 Champions League knockout matches against English sides (W16 D7 L1), with Leicester City's 2-0 win over Sevilla in March 2017 the only victory for an English team in that time.