Lluis Cortes’s side had done most of the hard work in the first leg, winning 3-0, and go through 4-2 on aggregate despite losing the return 2-1.
The hosts opened the scoring on 20 minutes when Janine Beckie prodded home to raise hopes of an unlikely comeback.
Barcelona produced a strong response to going behind with Asisat Oshoala twice denied an equalizer by Lucy Bronze on the goalline.
Oshoala finally made it 1-1 just before the hour mark, slotting into an empty net, to all but secure Barcelona’s place in the last four.
Manchester City went on to win the game through Sam Mewis’s penalty, but it’s Barcelona who progress to a semi-final against Lyon or Paris Saint-Germain.
You can check out the highlights below: