Mesut Ozil scored his first Arsenal goal as the Gunners beat Napoli in the Champions League, while Chelsea also secured three points as they saw off Steaua Bucharest.
Ozil, signed from Real Madrid for £42.5 million in the summer, opened the scoring with a stunning strike from Aaron Ramsey's cutback on eight minutes to set Arsenal on their way to a 2-0 triumph over Napoli.
The Germany international then turned provider seven minutes later as he crossed for Olivier Giroud, who converted past goalkeeper Pepe Reina to put the game beyond Rafael Benitez's team.
In the other Group F game, Borussia Dortmund marched to a 3-0 scalp of Marseille as Robert Lewandowski helped himself to a brace.
Lewandowski, who is reportedly set to join Bayern Munich next summer, broke the deadlock on 19 minutes and Marco Reus made it 2-0 in the second period.
The Poland international sealed the success from the penalty spot with ten minutes remaining to ensure they recovered from their opening defeat at Napoli.
Jose Mourinho's Chelsea bounced back from their opening Group E loss against Basel to run out 4-0 winners at Steaua Bucharest.
After seeing Fernando Torres go off injured on 11 minutes, Ramires handed the Blues the lead shortly after as he netted from close range.
The home side fell further behind when Daniel Georgievski scored an own goal, then Ramires notched his second of the game before Frank Lampard struck late to wrap up three points.
Elsewhere in Group E, promising youngster Julian Draxler was the match-winner for Schalke as they beat FC Basel 1-0 at St Jakob-Park.
Barcelona ground down Celtic as Cesc Fabregas scored the only goal of a game that finished 1-0 at Parkhead after Scott Brown was sent off on the hour mark.
Fabregas' goal came in the 75th minute as he met an Alexis Sanchez cross with a looping header that beat goalkeeper Fraser Forster.
Ajax's home game versus AC Milan ended in a 1-1 draw, and the contest was not without its drama.
With the scoreline goalless until the dying moments, Stefano Denswil's 90th minute strike appeared to hand the home side the victory.
But a controversial penalty awarded to Milan deep into injury-time was converted by Mario Balotelli to salvage a point.
In Group G, Atletico Madrid, who have enjoyed a fine start to the Liga season, recovered from a goal down to see off Porto 2-1 at Estadio do Dragao.
Jackson Martinez put Porto in front only for goals from Diego Godin and Arda Turan to turn the game on its head.
Earlier on Tuesday, Zenit St Petersburg and Austria Vienna picked up their first points of the campaign with a goalless draw in Russia.