Inter Milan striker Christian Vieri scored a dramatic last-minute winner against Dynamo Kiev at the San Siro in Italy.
Daniele Adani had given the home team the lead after 23 minutes before Sergei Fedorov scored a deserved equaliser for the visitors.
But just when it seemed as though Kiev would leave Italy with a valuable point, Vieri scored with a glancing header in the 90th minute.
The other Group B game saw Arsenal held to a goalless draw in Russia by Lokomotiv Moscow as both sides earned their first point of this year's competition.
Juventus were another Italian team to enjoy a successful night as they came back from a goal down to beat Group D rivals Olympiakos 2-1 in Greece.
The home side took a surprise lead when Ieroklis Stoltidis headed in on his Champions League debut from an 11th minute Christian Karembeu cross.
But the lead did not last for long as Pavel Nedved scored with a low free-kick and, after each team hit the post, the Czech playmaker scored a second after 79 minutes.
There were two away wins in Group D as Spain's Real Sociedad beat Galatasaray 2-1 in Turkey.
Darko Kovacevic had put the visitors ahead and Hakan Sukur equalised before Xabi Alonso was Real Sociedad's hero with a 71st minute winner.
Bayern Munich went a goal and man down but managed to salvage a 1-1 draw in Belgium against Anderlecht in Group A.
Claudio Pizarro was sent off for two yellow cards in quick succession in the first half and Anderlecht took the lead shortly after the interval through Ivica Mornar.
The other Group A match saw Celtic get off the mark with their first win of this season's Champions League as they beat French club Lyon at home.
Alan Thompson missed a penalty for the Scottish club before Swedish striker Henrik Larsson set up two goals as he crossed for Liam Miller and Chris Sutton to score.
In Group C, Monaco registered the biggest win of the night as a Fernando Morientes brace helped them dismiss AEK Athens 4-0.
Ludovic Giuly put the French side ahead before on-loan Real Madrid striker Morientes scored twice, with Dado Prso rounding off the win.
Deportivo also eased to victory as they had a Sergio opener and a Walter Pandiani penalty to thank for their three points against PSV Eindhoven.