Cristiano Ronaldo struck twice on his 400th game for Real Madrid as the Champions League title-holders won 3-1 at Borussia Dortmund.
In Cyprus, Harry Kane scored a hat-trick for Tottenham Hotspur in their 3-0 victory over Apoel Nicosia on Tuesday.
Manchester City, Porto, Napoli, Besiktas and Sevilla -- with three goals from Wissam Ben Yedder -- all earned victories, while Liverpool were held to a 1-1 draw at Spartak Moscow.
Holders Real, who had never won in Dortmund, shrugged off indifferent domestic form to make it two wins out of two in Group H.
Tottenham are also on maximum points in the group, while Bundesliga leaders Dortmund now have an uphill struggle after two defeats.
"It is a very proud night for myself and the team," Kane said.
"I try and score every game - it is a bonus when I get three."
In Dortmund, Gareth Bale brilliantly volleyed Real in front and provided the pass for Ronaldo, who was also playing his 150th European cup game, to score five minutes after the break.
Dortmund were back in the game when Pierre-Emerick Aubameyang turned in Gonzalo Castro's low cross in the 53rd minute.
But Ronaldo raced on to a Luka Modric pass to finish emphatically in the 79th for his second goal of the night -- his 112th in Europe and 411th for Real.
"We knew after so many years we'd finally win here one day and today was the day," Real captain Sergio Ramos said.
"We want to rediscover our best and I think tonight was a step in the right direction."
Dortmund midfielder Nuri Sahin told Sky TV: "Against Real Madrid you need your best day and we didn't have that today."
Manchester City remained unbeaten for a 10th Champions League home game with a 2-0 defeat of Shakhtar Donetsk to make it two wins from as many games in Group F.
Kevin de Bruyne broke the deadlock with an unstoppable shot from some 20 metres in the 48th minute..
City were denied a second goal when Sergio Aguero had a 72nd-minute penalty saved by keeper Andriy Pyatov, but substitute Raheem Sterling made sure of the result in the 89th.
Napoli draw level in the group with Shakhtar after a 3-1 victory over Australian goalkeeper Brad Jones's Feyenoord.
Lorenzo Insigne netted after seven minutes, Dries Mertens made it two shortly after the break and Jose Callejon scored a third.
The Dutch side failed to convert a penalty but netted a late consolation through Sofyan Amrabat.
Liverpool have drawn their opening two games after they came from behind to earn a point at Spartak Moscow in Group E.
Philippe Coutinho levelled after a Fernando free-kick put the Russians ahead.
"It's disappointing. We controlled the game from start to finish so we should win it comfortably," Liverpool captain Jordan Henderson told BT Sport.
Sevilla head the standings after a 3-0 win over visiting Maribor.
Ben Yedder scored twice before the break and made it three from the penalty spot seven minutes from time, to become the first player in the Spanish club's history to score a Champions League hat-trick.
Besiktas took charge of Group G with a 2-0 defeat of RB Leipzig -- in a match interrupted for 10 minutes by a part floodlight failure -- to make it two straight victories.
Ryan Babel opened the scoring for Besiktas in Istanbul before Brazilian midfielder Talisco headed the second shortly before the break.
Porto recorded an emphatic 3-0 win at Monaco to go second in the group, with Vincent Aboubakar bagging a brace.
DPA