Real Madrid passed an early test of its Champions League credentials under Jose Mourinho by defeating AC Milan, while Chelsea, Arsenal and Bayern Munich also notched up their third successive victories Tuesday to close in on the knockout phase.
Cristiano Ronaldo scored from a free kick then set up Mesut Oezil's goal inside 15 minutes as nine-time winner Madrid asserted its authority in Group G over seven-time champion Milan in a showdown of the European Cup's two most successful clubs.
"We needed to impose a strong rhythm on the game from the start by playing with the type of concentration these games deserve - and we did that," Ronaldo said.
Arsenal celebrated the night's biggest win by routing Shakhtar Donetsk 5-1 and Premier League rival Chelsea beat Spartak Moscow 2-0.
Bayern Munich, which lost last season's final, found it tougher against Cluj, coming from behind to win 3-2 in Group E, which also saw AS Roma stunned 3-1 at home by Basel.
Another convincing win for Madrid has heightened expectations at Santiago Bernabeu that Mourinho, who led Inter to the Champions League title in May, can not only take his new team beyond the last-16 for the first time since 2004 - but deliver its 10th victory in the competition - nine years after the last.
The Spanish leaders blitzed Milan's goal with 22 shots - but the goals came early, starting in the 13th minute with Ronaldo's free kick flying through a gap in the defensive wall.
Within a minute, the Portugal forward darted into the area before feeding the ball back to Oezil, whose shot came off Daniele Bonera's head to loop over goalkeeper Marco Amelia.
At the midway point in Group G, Madrid has a five-point lead over Milan and Ajax, which earned its first victory against Auxerre.
Demy de Zeeuw capitalized on sluggish defending to put Ajax ahead and Luis Suarez netted again before half time from close range. Valter Birsa curled in a free kick for Auxerre after Andre Ooijer was sent off for fouling Dennis Oliech, who was also later shown a second yellow card.
In Group F, Chelsea had to return to the scene of its defeat in the 2008 final, but left Moscow with far happier memories after securing the victory with goals in the first half from Yuri Zhirkov and Nicolas Anelka.
Yuri Zhirkov smashed in a spectacular volley from 25 yards and Anelka turned a defender and slotted neatly into the corner.
"We established good control in that first half, scoring two goals, and then controlled it defensively in the second," Chelsea manager Carlo Ancelotti said.
Chelsea has a three-point lead over Spartak and is a further three ahead of Marseille, which edged Zilina 1-0 in the other group match. Souleymane Diawara headed in Lucho Gonzalez's corner at the start of the second half.
It was a far less even contest in north London, where Alex Song fired Arsenal ahead in the 19th following an error by goalkeeper Andriy Pyatov.
Captain Cesc Fabregas marked his return from more than a month out with a hamstring injured with a goal from the penalty spot, while Samir Nasri, Jack Wilshere and Marouane Chamakh also netted for Arsenal.
"Let's not deduce too much, we have shown good quality but it is just the start, let's continue to improve," manager Arsene Wenger said. "The team has good potential."
Former Arsenal striker Eduardo da Silva scored a late consolation for the Ukrainian side, which remains second in Group H three points behind the Gunners.
Their next nearest challenger is third-placed Braga, which picked up its first points with a 2-0 win over Partizan Belgrade.
Rodrigo Lima scored from a free kick and substitute Luis Aguiar tapped in another near the end.
In Munich, Cluj threatened an upset when Cadu headed the Romanian visitors ahead in the 28th minute but the captain inadvertently deflected the ball into his own goal four minutes later.
Another own goal six minutes later - this time from Cristian Panin's clumsy deflection - put Bayern in control.
The German side finally scored for itself - helped by Cadu's poor defending - when Mario Gomez poked the ball through goalkeeper Eduard Stancioiu's legs in the 77th.
It was a nervy end for Bayern after Juan Culio pulled another back for Cluj, but the German side opened up a six-point lead over its Group E rivals, who all have three points.
Basel is second on goal difference after winning at the Stadio Olimpico. Alexander Frei, Samuel Inkoom and Cabral scored for the visitors, while Marco Borriello netted for Roma.
