Manchester United suffered a 1-0 defeat at Old Trafford against CFR Cluj but the Romanians had little to celebrate as Galatasaray qualified to the knockout stages stages beating Sporting Braga.
Celtic qualified to the last-16 beating Spartak Moscow 2-1 at home while Bayern Munich thrashed BATE Borisov 4-0 and Valencia won 1-0 over Lille.
Arsenal continued their winless run as they suffered yet another defeat at Olympiacos. Arsene Wenger's side lost 2-1 against the Greeks away from home nut have already secured a spot in the last-16.
Russians Zenit St Petersburg and Ajax qualified for the UEFA Europa League. Zenit beat AC Milan while Ajax, despite losing 4-1 to Real Madrid, claimed two Europa league spots.
PSG finished as Group A winners with a 2-1 victory over Porto while Malaga finished on top of Group C despite a 2-2 draw Anderlecht. Dortmund, who beat City 1-0 at home in a group D clash, emerged as group winners while Real Madrid ended second.
UEFA Champions League 2012/13 (Tuesday's results):
Olympiakos Piraeus 2-1 Arsenal
Dinamo Zagreb 1-1 Dynamo Kyiv
PSG 2-1 Porto
Montpellier 1-1 Schalke 04
Malaga 2-2 Anderlecht
Milan 0-1 Zenit
Borussia Dortmund 1-0 Manchester City
Real Madrid 4-1 Ajax
Barcelona 0 - 0 Benfica
Chelsea 6 - 1 Nordsjaelland
Manchester United 0 - 1 CFR Cluj
Shakhtar Donetsk 0 - 1 Juventus
Lille 0 - 1 Valencia
Bayern Munich 4 - 1 BATE
Celtic 2 - 1 Spartak Moscow
Sporting Braga 1 - 2 Galatasaray