Inzaghi's men will now face the winner of the other UCL semi-final tie between Arsenal and PSG tomorrow.
The breakthrough came when Barcelona lost possession in midfield in the 21st minute, allowing Federico Dimarco to launch a quick counter.
Barcelona were very close in getting the winner on the night as Yamal was brought down by Mkhitaryan close to the penalty area with the referee pointing to the spot.
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