Atletico Madrid made it three wins from three, thanks to a double from in-form striker Diego Costa in a 3-0 victory at Austria Vienna, leaving the Spanish side on the brink of the last 16 already to continue its brilliant start to the season.
Chelsea claimed the performance of the night by crushing Schalke 3-0, with striker Fernando Torres also scoring twice to put the 2012 champions top of Group E.
Robert Lewandowski grabbed an 82nd-minute winner for Dortmund, last season's beaten finalist, at Arsenal in Group F to bring the English team down to earth after a flying start to the Premier League and in Europe.
They are joined in a three-way tie on six points by Napoli, which won 2-1 at Marseille to condemn the French side to a third straight loss.
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There were also first wins of the group stage for Celtic and Zenit St. Petersburg while Basel drew 1-1 at Steaua Bucharest.
There was no shortage of stars on show at the San Siro and two of them combined for Milan's opener, Robinho exchanging passes with Kaka before slotting past Victor Valdes.
However, Milan has never been able to handle Messi, the Argentina forward has now scored six times against the Italians, and he equalized after collecting Andres Iniesta's pass, evading Kevin Constant and shooting into the bottom corner.
The teams meet again in two weeks' time, with Barcelona knowing a victory would put them on 10 points and close to the knockout stage.