Mesut Ozil showed his playmaking pedigree to orchestrate Arsenal's 2-0 victory over Napoli while a late Cesc Fabregas header gave Barcelona a hard-fought 1-0 win at 10-man Celtic in the Champions League on Tuesday.
Both sides have six points from their opening two games, as do Atletico Madrid with their Turkey midfielder Arda Turan netting an 86th minute winner in a 2-1 victory at Porto.
Julian Draxler's sweet strike just after the break was enough to beat Basel and maintain Schalke 04's perfect start.
Borussia Dortmund's Poland striker Robert Lewandowski scored twice in s 3-0 demolition of Olympique Marseille as did Chelsea's Brazilian Ramires to get their campaign up and running in a 4-0 win at Steaua Bucharest after a shock opening home defeat by Basel.
There was also late drama in Amsterdam with Stefano Denswil heading Ajax ahead in the last minute, only for Mario Balotelli to level with a penalty in the fourth minute of stoppage time in a 1-1 draw.
Ozil has quickly impressed since his big-money move from Real Madrid last month and he again oozed class at the Emirates as Arsenal took control of Group F by easing past a Napoli side tasting defeat for the first time under coach Rafael Benitez.
The German international opened his account for the London club with a sweet strike from the edge of the box after eight minutes.
He then set up Oliver Giroud for a second soon after in a display that left manager Arsene Wenger searching for superlatives.
"Ozil was absolutely amazing in the first half, fantastic. Individual skill, finishing, it was all fantastic and was what you dream to see in the stand when you come and watch football," Wenger said.
The result meant Premier League leaders Arsenal made it 10 wins in a row in all competitions, including a League Cup penalty shootout success.
Barca, who surprisingly lost to Celtic at Parkhead in the group stage last season and on Tuesday were without injured World Player of the Year Lionel Messi, had to work hard for their Group H victory in Glasgow.
The task was made easier when Celtic captain Scott Brown was sent off just before the hour for kicking out at Neymar after the Brazilian had tumbled under his challenge.
Barca, without Messi's magic, had probed but mostly huffed and puffed all night until they made their numerical advantage pay 14 minutes from time with Neymar involved in the build-up.
His lay off found substitute Alexis Sanchez on the right flank and the Chilean's cross was met by Fabregas who headed past Fraser Forster.
Chelsea lost striker Fernando Torres with an early knee injury but Jose Mourinho's men were far too strong for Steaua with winger Andre Schuerrle instrumental in getting the 2012 European champions up and running in Group E.
The German had a hand in the first and third goals scored by Ramires, with a Daniel Georgievski own goal and a late Frank Lampard strike rounding off a comfortable win.
"Schuerrle was fundamental. We identified what we had to do to penetrate their defence," said Mourinho.
"He was the man for that. He was in the position where we knew we could (have success) and we played from there."
Atletico Madrid came into their Group G match in Porto on a high after stunning Real Madrid 1-0 at the Bernabeu on Saturday to keep up a perfect record in La Liga after seven games, but they fell behind after 16 minutes on Tuesdsay when Colombian Jackson Martinez scored with a diving header.
However, Atletico coach Diego Simeone has forged a highly motivated unit and the Spaniards battled back after the break.
Uruguayan defender Diego Godin climbed high to head home in the 58th and the visitors took home the points when Gabi slotted a clever short free kick into the area for Turan to blast home.
Ajax thought they had their first victory in Group H when central defender Stefano Denswil rose unchallenged to head home a corner in the 90th minute but a controversial Balotelli equaliser soon quashed the celebrations.
Mike van der Hoorn was penalised for tangling with Balotelli and the Italy striker kept his cool from the spot to put Milan on four points, two behind Barca.
Borussia Dortmund coach Juergen Klopp watched from the stands as he served a one-match touchline ban but he was soon punching the air after Lewandowski capped a counter-attack with the opening goal after 19 minutes against Marseille in Group F.
Marco Reus added a second after the break from a free kick that caught out Marseille keeper Steve Mandanda and Lewandowski sealed victory with a 79th-minute penalty to put last season's beaten finalists level on three points with Napoli.
Environmental protesters briefly held up Basel's Group E clash with Schalke when they dropped down on cables from the stadium roof and unfurled a huge yellow Greenpeace banner.
A spokesman for organisers UEFA said the incident would be reported and disciplinary proceedings could be launched.
The only goal came when a partially cleared corner fell to Draxler 25 metres out and, although it bounced to him at an awkward height, he struck a superb rising shot into the top corner in the 54th minute.
In the day's early kick off, 10-man Zenit St Petersburg were held to a 0-0 draw at home by Austria Vienna in Group G.
Hulk hit the woodwork for the hosts but Zenit's hopes were hindered by Belgian midfielder Axel Witsel's dismissal for a rash challenge a minute before halftime.