While Lionel Messi and Co dominated possession throughout the game, Milan's Kevin Prince Boateng and Sulley Muntari scored to set up an amazing return leg clash at the Nou Camp.
First-half remained quiet as Milan waited in their own half to deny Barca an early goal. Messi, the World Player of the Year, was not given too much space to wriggle and lost possession more often.
Just before the hour mark, Montolivo's shot came off Cristian Zapata's arm before Boateng fired towards the right hand side to give Milan the lead.
Barcelona continued to try and create chances with their dominating style of play but it was Milan who took a surprise two-goal lead. Substitute striker M'Baye Niang and forward El Shaarawy combined on the right to set up Muntari, who slammed in a volley to the far corner.
Galatasaray 1-1 Schalke
Schalke return with a slight advantage over the their Turkish opponents in the second leg after Jermaine Jones late strike in the first half cancelled out Burak Yilmaz's opener.
Didier Drogba and Wesley Sneijder reutrned to the Champions League following their recent moves to Gala from Shanghai Shenhua and Inter Milan respectively.
Yilmaz's opening goal was a moment of magic as the forward collected the ball on the edge of the area before flicking the ball past defender Benedikt Howedes and firing home in the 12th minute.
but their lead lasted until the end of the first half as Farfan crusied through on goal after the home side lost possession in midfield and laid the ball to Jones to smashed on goal with ease.