Holders Real Madrid swept aside Basle 5-1 to open the defence of their Champions League crown in style at the Bernabeu.
The Spaniards bounced back from successive domestic La Liga defeats to rout the Swiss, who fell behind to an own goal from Marek Suchy (14) when the defender put a cross from Nacho into his own net.
Wales forward Gareth Bale made it 2-0 on the half hour with a superb finish over the goalkeeper after being put in by Luka Modric, with Cristiano Ronaldo (31) slotting home a third moments later and then £70million Colombian hitman James Rodriguez (37) sweeping in a fourth.
Derlis Gonzalez (38) netted a consolation on the break, before Karim Benzema (79) completed the comprehensive victory late in the second half, crashing his shot off the bar following another quick counter as Real stormed to the top of Group B.
At Anfield, Liverpool needed a stoppage-time penalty from captain Steven Gerrard to give the Reds a 2-1 win over Ludogorets on their return to the Champions League for the first time in five years.
Mario Balotelli (82) looked to have won it with a first Liverpool goal since his £16million summer transfer from AC Milan, only for substitute Dani Abalo to level for the unheralded Bulgarians in the 90th minute before Gerrard converted from the spot after Javier Manquillo had been tripped by goalkeeper Milan Borjan.
Arsenal's Group D campaign got off to the worst possible start as the Barclays Premier League side were beaten 2-0 at Borussia Dortmund.
Ciro Immobile (45) and Pierre-Emerick Aubameyang (48) both made the most of some poor Gunners' defending either side of half-time to give Jurgen Klopp's side a well-deserved victory.
In Istanbul, Galatasaray striker Burak Yilmaz netted a stoppage-time equaliser to deny Anderlecht a first away Champions League win for nine years.
Anderlecht - who have finished bottom in all seven group stage campaigns since they reached the last 16 in 2000/01 - looked to be on course for a hard-earned victory after taking the lead early in the second half through Dennis Praet.
Aleksandar Mitrovic missed a great chance to make it 2-0 moments later, which ultimately proved costly as Yilmaz crashed home following a powerful run by Aurelien Chedjou to earn the hosts a share of the points.
In Group A, Carlos Tevez scored both goals in Juventus' 2-0 win over Malmo.
The Argentine former Manchester United and City forward ended his long European goal drought with a first since 2009 after a neat finish just before the hour, and then added another with a late free-kick.
Olympiacos top the table after beating last season's runners-up Atletico Madrid 3-2 at the Georgios Karaiskakis Stadium.
Arthur Masuaku (13) and Ibrahim Afellay (31) looked to have put the Greeks in control.
Croatian striker Mario Mandzukic (38) got Atletico into the tie again before half-time with a goal on his Champions League debut, but Kostas Mitroglou - loaned back from Fulham - restored the two-goal cushion with 17 minutes left.
Antoine Griezmann (86) set up a nervy finish, but the home side saw out the closing stages for what could yet prove a valuable victory.
In Group C, Zenit St Petersburg recorded a 2-0 win away at 10-man Benfica.
Brazilian Hulk set Andre Villas-Boas' men on their way after just five minutes, before, on 18 minutes, Benfica goalkeeper Artur was shown a red card for a professional foul on Danny.
After former Benfica midfielder Axel Witsel (22) headed in a second goal, it was damage limitation for the Portugese side.
Monaco, back in the Champions League group stages for the first time since the 2004-05 season, secured a 1-0 win over Bayer Leverkusen at the Stade Louis II with a second-half goal from Joao Moutinho.