Madrid - Holders Real Madrid and 2013 finalists Borussia Dortmund scored impressive away wins early Thursday (Thailand time) in the Champions League.
Real Madrid's Cristiano Ronaldo (R) defends during a corner by Liverpool. (EPA photo)
Real won 3-0 at Liverpool - with their first-ever goals against the Reds - and Dortmund cruised 4-0 at Galatasaray.
Karim Benzema was Real's hero in their 3-0 win in Liverpool with a first-half brace, after Cristiano Ronaldo gave the whites an early lead with his first-ever goal at Anfield.
Liverpool looked shaky in defence, and goalkeeper Simon Mignolet was at fault on two of the goals. They managed to tighten up in the second half but rarely threatened to turn the tie around, despite Philippe Coutinho hitting the woodwork.
"We have to keep on this run of winning, winning and winning. The biggest positive we can take is that we are comfortable playing in any tactical system," veteran Real goalkeeper Iker Casilas said.
"We know that we have a great team, and that is going to keep us going until the end of every game."
Real are bidding to become the first team since AC Milan in 1990 to successfully defend the European crown.
Their coach, Carlo Ancelotti, said: "It was the best we have played all season. We were fantastic in the first half and then controlled the game. I had to say nothing to the players - they played really well.
"I am lucky to manage this group of players. ... We defended well in the first 20 minutes when Liverpool played with good intensity. It was all over at half-time."
Liverpool manager Brendan Rodgers said his side was "excellent" for the first 22 minutes, before Real Madrid took over.
"They were terrific. Second half we played for pride, and we were outstanding, the players kept going, they didn't stop. We defended poorly, but I can't ask any more," he said.
"You can see Real's quality. Speed, technique - you can see why they are champions."
The other Group B game was a late 1-0 home win for Ludogorets over Basel on a last-minute goal from Yordan Minev.
Real are well clear atop the group with the maximum nine points from three games. The other three teams are tied on three points apiece.
In Group D, Arsenal scored a memorable late 2-1 comeback, as did Anderlecht, who went ahead against the run of play through Andy Najar. Late goals from Kieran Gibbs and supersub Lukas Podolski gave the Gunners an unlikely but not completely undeserved win.
"In the last five minutes in the Champions League the nerves play a part, and we had to get into these five minutes without conceding a second goal," said Arsenal boss Arsene Wenger, for whom the victory was a 65th birthday present.
"I had hope, it maybe didn't look like it, but it happened. It's a little bit of a gambling situation in these games, and it worked. I'm a bit disappointed that we didn't create more chances than we did but Anderlecht played well."
In Istanbul, in the group's other game, Dortmund enjoyed a 4-0 romp at Galatasaray with two early goals from Pierre-Emerick Aubanmeyang, plus scores from Marco Reus and Adrian Ramos.
The same as Real, Dortmund have the maximum nine points. Arsenal are on six, while Anderlecht and Galatasaray have one each.
Atletico Madrid caned feeble Malmo 5-0 in Group A, with second-half goals from Koke, Mario Mandzukic, Antoine Griezmann, Diego Godin and Alessio Cerci.
Malmo managed to get through to half-time with 0-0, but caved in after the interval.
"It was difficult to open up their defence, but after the first goal everything was much easier. ... We are now in a good position with six points," said the promising Koke.
In the group's other game, Olympiacos edged struggling Juventus 1-0 on a goal from Pajtim Kasami.
Olympiacos and Atletico are joint top on six points, while Juventus and Malmo have three each.
In Group C, Bayer Leverkusen beat Zenit 2-0 thanks to strikes from Giulio Donati and Kyriakos Papadopoulos - despite the sending-off of Borges Wendell. Meanwhile, Benfica battled out a 0-0 draw at Monaco.
Leverkusen have six points, Monaco five, Zenit four and Benfica one.