United had overcome a two-goal deficit at Paris St Germain last month but Messi’s first-half brace and a wonder strike from Philippe Coutinho ushered Barcelona towards a 3-0 victory, 4-0 on aggregate, at the ground of one of the Premier League side’s greatest triumphs.
Ole Gunnar Solskjaer was insistent that the 1999 Champions League final win over Bayern Munich would have no bearing on this quarter-final second leg and his remarks proved accurate.
While his side made an energetic start, with Marcus Rashford denied by the goal frame within seconds of kick-off, Barcelona became more proactive and Messi, as he so often has done in the past, took top billing.
The 31-year-old five-time Ballon d’Or winner was largely subdued in Barcelona’s 1-0 victory at Old Trafford last Wednesday and had his nose bloodied after being caught unintentionally by Chris Smalling’s flailing arm.
But he doubled Barcelona’s advantage with a left-footed strike from the edge of the area that has so often become his hallmark, although his second strike arrived following a major blunder from United goalkeeper David De Gea.
There was nothing the United goalkeeper could do to stop Coutinho just after the hour mark, though, as Barcelona – after three last-eight exits in as many seasons – booked a semi-final showdown against either Liverpool or Porto.
For United, who were looking to reach the last four in this competition for the first time since 2011, their attentions now turn to the Premier League and a battle to finish in the top four.
They at least started with plenty of belief, with boss Solskjaer preaching the virtues of having an attacking mindset in an intimidating atmosphere, a message his players seemed to take on board as they sprung out of the traps.
Rashford was able to get in behind the Barcelona defence but saw his toe-poke clip the top of the bar in the opening seconds, while Scott McTominay dithered in space moments later, allowing the hosts to clear their lines.
United’s inability to take their chances at Old Trafford – where they did not have a single shot on target – had frustrated Solskjaer and their failure to do so here emboldened Barcelona.
The visitors were given a let-off when a penalty was rescinded after the video assistant referee deemed Fred had got a touch to the ball before Barcelona midfielder Ivan Rakitic went over the trailing leg.
The decision left Barcelona fans incensed but boos turned to cheers as an archetypal Messi goal after 16 minutes gave United an even bigger mountain to climb.
Ashley Young was caught in possession, allowing the Barcelona captain to nutmeg Fred and cut in-field from the right before curling a left-foot shot from the edge of the area beyond De Gea.
If the Spaniard could do little about that, he was entirely culpable four minutes later, allowing Messi’s tame right-foot effort to slide under him after United had once again given the ball away deep inside their own half.
Messi’s brace left United needing three goals to progress but the vigour they showed in the opening stages had evaporated, while they were fortunate not to fall further behind on the stroke of half-time.
De Gea made amends for his earlier mistake with a fantastic reflex save to keep out Sergi Roberto’s sliding finish at the back post from point-blank range.
The half-time break seemed to do little to raise United’s spirits and any realistic hope of a comeback disappeared when former Liverpool forward Coutinho exquisitely found the top corner from 25 yards after 61 minutes.
An overhead from Messi went just wide in front of an increasingly jubilant 96,708-strong crowd – Barcelona’s highest attendance of the season.
The pace of Rashford kept Barca’s defence honest but his withdrawal – with the more powerful Romelu Lukaku introduced after 73 minutes – suggested Solskjaer’s thoughts are now on the domestic front.
Former Barcelona forward Alexis Sanchez also came on in the closing stages for his first appearance in six weeks after a knee injury.
His header produced a brilliant full-length diving save from Marc-Andre ter Stegen, depriving United of a consolation.