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Paris St Germain beat Dynamo Kiev 4-1 on their return to the competition after eight years, with Zlatan Ibrahimovic again on the scoresheet.
Former Champions League holders Porto won 2-0 at Dynamo Zagreb with Lucho Gonzalez and Steven Defour scoring near the end of the first and second half respectively.
Klaas-Jan Huntelaar scored the winner as Schalke began their Champions League campaign with a 2-1 win away at Olympiacos.
Arsenal rode their luck to beat French champions Montpellier 2-1 away after conceding an early penalty.
Seven-times European champions AC Milan were booed off after a 0-0 home draw against Anderlecht at the San Siro.
Newcomers Malaga beat Zenit St Petersburg 3-0 at La Rosaleda with Isco netting a brace.
Real Madrid fashioned a stunning comeback to beat Manchester City 3-2 in a classic Champions League match with a last-gasp Cristiano Ronaldo strike in their Group D opener.
In a clash of ex-European title winners, Borussia Dortmund beat Ajax 1-0 in Germany, Robert Lewandowski striking late to seal victory