The Rossoneri produced the fifth-fastest Champions League goal ever when Alexandre Pato received a pass from Antonio Nocerino and fired home from outside the area inside the first minute.
In the other Group H match, Champions League debutants Viktoria Plzen were held to a 1-1 draw by Belarus outfit BATE Borisov with Marek Bakos edging the Czechs ahead in stoppage time of the first half before Renan Bressan answered for the visitors.
Chelsea took a while to get going at Stamford Bridge in Group E but eventually managed to record a 2-0 victory over Bayer Leverkusen thanks to second half goals from David Luiz and Juan Mata whilst CL newcomers Genk and Spaniards Valencia played out a 0-0 draw in Belgium.
Group F action saw Arsenal hold German Bundesliga champions Borussia Dortmund to a 1-1 draw at Signal Iduna Park with the home side grabbing a point thanks to a brilliant late Ivan Perisic goal which canceled out Robin van Persie’s quality first-half strike.
Lucho Gonzalez struck the only goal of the game as French outfit Marseille scored a 1-0 away win at Greek club Olympiakos whilst in Group G, Cypriot club APOEL Nicosia came from behind to beat ten-man Zenit St Petersburg 2-1 with all goals coming in the second half.
And to round out the opening night of matches, reigning Europa League champions FC Porto kept their winning run going in Europe with a come-from-behind 2-1 win over Shakhtar Donetsk in the other Group G match.
Hulk and Kleber provided the goals for the Portuguese side whilst Luiz Adriano was on target for the Ukrainians who had two men sent from the pitch.
2011/12 UEFA Champions League group stage – Tuesday, September 13
Genk (BEL): 0
Valencia (ESP): 0
Cristal Arena, Genk
Olympiakos (GRE): 0
Olympique Marseille (FRA): 1 (Lucho Gonzalez 51’, red card: Rod Fanni 90+1’)
Karaiskakis Stadium, Athens
APOEL Nicosia (CYP): 2 (Gustavo Manduca 73’, Ailton Almeida 75’)
Zenit St Petersburg (RUS): 1 (Konstantin Zyryanov 63’, red card: Bruno Alves 76’)
GSP Stadium, Nicosia
Viktoria Plzen (CZE): 1 (Marek Bakos 45+1’)
BATE Borisov (BLR): 1 (Renan Bressan 69’)