United came into the game at the Camp Nou looking to emulate their last-16 heroics when they made history by overcoming a 2-0 first leg deficit to dump out Paris Saint-Germain on away goals rule.
And, while they only had to come back from being one goal behind in Spain, Barca’s record on home soil in Europe looked daunting as they had gone 30 games unbeaten without conceding more than one goal in any of those fixtures.
United survived an early penalty decision, which was overturned by the Video Assistant Referee (VAR), but there relief was short-lived as Lionel Messi virtually killed the tie off with two goals inside the opening 20 minutes to leave the aggregate score at 3-0.
Philippe Coutinho put the icing on the cake just after the hour mark with a stunning strike as Barca eased into the semi-finals.
Manchester United boasted three changes from the 1-0 first leg as Phil Jones, Jesse Lingard and Anthony Martial replaced Luke Shaw, Diogo Dalot and Romelu Lukaku.
Hosts Barcelona made just one change from last week's game at Old Trafford as Sergi Roberto came in for Nelson Semedo.
United made a strong start with Marcus Rashford going close inside the opening minute when he latched on to a ball through from Paul Pogba and toe-poked his effort clipped off the crossbar.
Scott McTominay almost went through on the Barca goal but a poor first touch saw the ball run away from him and the hosts managed to clear their lines.
Barca were awarded a dubious spot-kick in the 10th minute when the referee adjudged that Fred had fouled Ivan Rakitic inside the area, but the decision was overturned when the match official consulted with VAR.
However, United did find themselves a goal behind within six minutes when Ashley Young gave away possession in the left-back position and Messi nipped in to take the ball past Fred before hitting a superb low strike past David De Gea from the edge of the area.
It was 2-0 in the 20th minute when Messi tried his luck from just outside the area and, while it appeared to be a comfortable save for De Gea, the United custodian uncharacteristically allowed the ball to squirm through his grasp and into the net.
The second goal knocked the stuffing out of the Red Devils and it was Barca who looked like adding more goals to their tally.
Rakitic forced De Gea into a low save with a downward header from a free-kick, before the United shot-stopper made amends for his earlier error with a vital save to deny Roberto the chance to convert a Jordi Alba cross at the back post in first half stoppage time.
Messi went close to his hat-trick two minutes into the second half when he got on the end of a Luis Suarez pull-back, but his effort was deflected wide off Young.
United did enjoy a spell of possession without troubling their hosts, before Countinho ended any hopes of a comeback on 61 minutes when he picked up a pass from Alba, cut inside and curled a wonderful right-foot strike from 25 yards into the far corner.
Messi almost grabbed his third of the night on 64 minutes with an audacious overhead kick which dropped just wide of De Gea’s goal.
Barca continued to dominate proceedings, although Lingard almost gave Ole Gunnar Solskjaer’s men a consolation goal on 79 minutes when he hit a drive from 20 yards which dipped just over the crossbar.
Suarez looked to get amongst the goals on 88 minutes when he got a yard on Fred and chipped the ball over De Gea but watched a sit dropped on to the top of the net.
Marc-Andre ter Stegen had very little to do in the game, but he pulled off a fine save in the last minute to deny Alexis Sanchez a goal against his former club with a header from Dalot’s cross.