Double from Lionel Messi and a stunning goal from Philippe Coutinho was the Spanish giants needed to secure victory over the Premier League side.
Barcelona came into the game with a slim advantage over the Red Devils after winning the first leg 1-0 courtesy thanks to an own goal from Luke Shaw.
Barcelona broke the deadlock just 16 minutes into the game. Messi punished Young for a costly mistake at the back, burying a left-footed strike into the bottom corner.
Ashly Young lost the ball under pressure at left-back and it travels to Messi on the edge of the box. He drops a shoulder to beat the challenge of Smalling before bending his effort around De Gea into the net.
The Argentine grabbed a double 4 minutes later as De Gea allowed a trickling strike from Messi on his right foot through his grasp into the bottom corner.
16 minutes into second half, Coutinho gives Barcelona a three goal lead with an absolute stunner which ripped into the back of the net.
He collected an offload 25 yards from goal before advancing to the edge of the box, gets half a yard on Smalling and it was enough to allow him to strike a perfect ball into the top corner, beating the hand of De Gea.
A comfortable victory for Barcelona as they secured semi-final spot.