The heavyweight clash of the night saw reigning champions Barcelona held by Inter Milan as Dynamo Kiev came from behind to beat Rubin Kazan.
Lyon started on a winning note after beating Fiorentina, Sevilla saw off Unirea Urziceni and Olympiakos edged out AZ Alkmaar.
Eduardo scrambled a late winner for Arsenal as Arsene Wenger's side came back from two goals down to win 3-2 away to Standard Liege.
The Belgian champions were 2-0 up inside five minutes following goals from Eliaquim Mangala and Milan Jovanovic's penalty, but Nicklas Bendtner pulled a goal back on the stroke of half-time.
Thomas Vermaelen levelled matters on 78 minutes and three minutes later Eduardo, who was only cleared to play earlier in the week, nudged the ball home from close range.
Olympiakos' new coach Zico watched from the stands as the Greek side overcame AZ Alkmaar 1-0 in a lifeless encounter in Group H's other match.
In a game of few chances, Olympiakos grabbed the only goal on 79 minutes when Vassilis Torosidis rose to head home Jaouad Zairi's cross from the right.
Liverpool made a winning start to Group E, but were forced to work hard to overcome Champions League debutants Debrecen 1-0 at Anfield.
The only goal of the game arrived at the end of the first half when Dirk Kuyt tucked away the loose ball after Fernando Torres' shot had been saved.
Lyon also made a winning start to the group with a 1-0 success over 10-man Fiorentina at Stade Gerland.
Alberto Gilardino was sent off in first-half stoppage-time for elbowing Jeremy Toulalan and Miralem Pjanic bundled home the winner for Lyon on 76 minutes.
Rangers picked up an excellent point on their travels after coming from behind to grab a 1-1 draw at Stuttgart.
Pavel Pogrebnyak put Stuttgart ahead after 18 minutes, but Madjid Bougherra atoned for his weekend red card by firing home a crisp equaliser 13 minutes from time.
Sevilla set the early pace in Group G after a 2-0 win at home to Unirea Urziceni, with the Romanian side playing their first game in the group phase.
Luis Fabiano slotted home from the edge of the area just before the interval to give Sevilla the lead and Renato headed home from close range for the second on 70 minutes.
Holders Barcelona were stifled in the San Siro as Jose Mourinho's Inter Milan opened up Group F with a 0-0 draw.
Barcelona dominated possession away from home and came closest to scoring, but Dani Alves was unable to find the back of the net.
Dynamo Kiev came from behind to win 3-1 at home to Rubin Kazan, with the Ukrainians scoring three times in the final 20 minutes.
Alejandro Dominguez's free-kick gave Rubin a first-half lead, but goals from Ayiila Yussuf, Gerson Magrao and Oleg Gusev tipped the tie in Kiev's favour.