Barca took a one-goal advantage to Camp Nou after they beat Man Utd 1-0 at Old Trafford last week.
On Tuesday, Barca finished the job at home by cruising past the visitors 3-0 on the strength of two goals from Lionel Messi.
Barca were also helped by a shocking howler from Man Utd goalkeeper David de Gea, which accounted for the team and Messi's second goal on the night.
The four-goal defeat meant Man Utd have now lost on aggregate by four or more goals in a two-legged European knockout tie for the first time in their history.
The club's previous heaviest defeats on aggregate were a 5-2 loss to Milan in the 1957-58 European Cup semi-final, and a 4-1 reverse against Atletico Madrid in the last 16 of the 1991-92 Cup Winners’ Cup.
Tuesday's defeat continued a torrid run of form for Man Utd, who have now lost five of seven games in all competitions since their stunning win at PSG in the last-16 second leg.
Ole Gunnar Solskjaer's side have now lost four consecutive away matches in all competitions for the first time since October 1999.
Solskjaer himself played in all four of those defeats nearly 20 years ago.
With their European dreams dashed, Man Utd will now return to their pursuit of a top-four spot in the Premier League.