The Spanish outfit had the lead on the night inside five minutes when Lionel Messi struck from the edge of the box, before the Argentine added his second to level the tie at 2-2 moments before the interval.
The Italian side pushed for the goal that would have taken them into the next round in the latter stages, but they were stung on the counter as Jordi Alba made it 4-0 on the night in stoppage time.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
BARCELONA: Valdes; Alves, Pique, Mascherano, Alba; Busquets, Xavi, Iniesta; Pedro, Messi, Villa
AC MILAN: Abbiati; Abate, Mexes, Zapata, Constant; Montolivo, Ambrosini, Flamini; Boateng; Niang, El Shaarawy