Barcelona were given a scare before overcoming Spartak Moscow, and Bayern Munich also got their Champions League campaign off to a winning start.
Lionel Messi scored twice to rescue Barcelona at the Camp Nou, while last year's losing finalists Bayern saw off Valencia in Germany.
There were away wins for BATE Borisov and CFR Cluj as they beat Lille and Braga respectively.
Shakhtar Donetsk also won, beating debutants FC Nordsjaelland.
2-0 victory put them top of the group, as
holders Chelsea were held to a 2-2 draw by Italian champions Juventus.
Mkhitaryan at the double
- Henrikh Mkhitaryan's double for Shakhtar means he has now scored twice in five matches this season.
Henrikh Mkhitaryan put Shakhtar in front when he drove in a shot just before half-time to break Danish side
The attacking midfielder added a second when his cross rebounded back to him and he sidefooted home for his 14th goal of the season.
have shown no hangover from losing last year's Champions League final to Chelsea as they won a fifth game on the trot with a 2-1 victory over
Bastian Schweinsteiger's deflected shot and a rifled effort by Toni Kroos helped Bayern to victory, Valencia substitute Nelson Valdez heading the Spanish side's reply in injury time.
Barcelona coach Tito Vilanova
“"To start off with a win is very important. I can't say that I am pleased with the performance but as for the defence it is always possible that you can concede if you are so far up the pitch."”
Late in the game, the visitors' centre-back Adil Rami was sent off for a second yellow card after bringing down Arjen Robben, although Mario Mandzukic saw his penalty saved.
top the group after putting in an impressive performance to win 3-1 at
and secure their first ever win in the Champions League group stages.
Aleksandr Volodko turned and powered in a long-range strike, Vitali Rodionov tapped home after a swift counter-attack and Edgar Olekhnovich fired in to score the goals for the ruthless Belarus outfit.
Lille wasted a number of chances and had only an Aurelien Chedjou header to show for their efforts.
once again had Messi to thank as they beat Russian side
Messi matches Raul
- This is the 14th time Messi has scored at least twice in a Champions League match, equalling a record held by Raul.
The Spaniards took the lead when Cristian Tello cut in on to his right foot and bent in a powerful shot only for a Dani Alves own goal and a cool finish from Romulo leave them trailing.
But Tello turned provider to the cut the ball back for Messi, who scored a late header to save Barcelona's blushes and add a ninth goal in seven games this season.
Celtic and Benfica played out a goalless draw
in the group's other game.
Manchester United secured a 1-0 victory over Galatasaray
at home, while Rafael Bastos came back to haunt former side
as his two goals gave
Modou Sougou slid a pass through for Bastos to slot in the opener against the Portuguese club.
The forward added a second when he came in from the left wing and past three defenders before driving in a low shot to secure victory for the Romanian side.