Defending European champions Chelsea had to settle for a 2-2 draw at home to Juventus after losing a two-goal lead at Stamford Bridge.
Oscar, on his first start for the club, broke the deadlock on 31 minutes as his strike took a deflection from Leonardo Bonucci that saw it sail past goalkeeper Gianluigi Buffon, who was making his 400th appearance for Juve.
The Brazilian then grabbed his second of the night in style. Receiving a pass from Ashley Cole, the 21-year-old spun away from his two markers before curling into the top corner. However, Chelsea's two-goal lead last just five minutes as Arturo Vidal fired low past Petr Cech.
With ten minutes remaining, substitute Fabio Quagliarella found an equaliser as he slipped the ball under the goalkeeper following a misplaced pass from John Obi Mikel. The visitors might have been ahead six minutes later as Quagliarella turned on the edge of the box, but his shot clipped the top of the bar.
Barcelona had to come from behind to see off Spartak Moscow 3-2 at the Camp Nou.
Barca looked to be on their way to a straightforward victory when Cristian Tello curled home the opener, but Dani Alves scored an own goal before Romulo gave the Russians the advantage on 58 minutes when netting from a tight angle.
However, Lionel Messi then equalised from close range and then, in the 80th minute, restored his side's lead with a header.
Manchester United claimed a nervy 1-0 win over Galatasaray.
The hosts took the early lead when Michael Carrick went past goalkeeper Fernando Muslera to fire home, but that lead could have been quickly squandered as Nordin Amrabat struck the bar after a charge down the left flank.
United had the chance to double their advantage early in the second half as Rafael was felled in the penalty area, but Muslera saved Nani's spot kick. Darren Fletcher later made his return from illness as a substitute as United clung on for victory.
Bayern Munich secured a 2-1 victory over Valencia at the Allianz Arena.
Bayern had last tasted Champions League action at the stadium when losing to Chelsea in last season's final, but they returned to winning ways as Bastian Schweinsteiger and Toni Kroos put them two goals up before Nelson Valdez's late header.
Celtic made a positive return to Champions League group action as they held last season's quarter-finalists Benfica to a 0-0 draw at Parkhead.
BATE Borisov secured an upset as they defeated Lille 3-1 in France.
Alexander Volodko scored a well-taken opener on six minutes and, after further goals from Vitaly Rodionov and Edgar Olekhnovich, the Belarusian champions had all but wrapped up the game by half-time.
Aurelien Chedjou reduced the deficit in the second half but Lille were unable to produce a comeback.
Shakhtar Donetsk secured a 2-0 win over FC Nordsjaelland to move ahead of Chelsea and Juventus in Group E. Henrikh Mkhitaryan scored both goals for the 2009 UEFA Cup winners.
Romanian side CFR Cluj claimed a surprise 2-0 win away to Braga.
Former Braga striker Rafael Bastos netted a brace while goalkeeper Mario Felgueiras, who left the Portuguese side this summer, put in an inspired display against the hosts.