Ramires scored twice to help Chelsea get its Champions League campaign back on track following a surprise 2-1 home defeat by Basel to open Group E.
"We played good football with intelligence and maturity," Chelsea manager Jose Mourinho said.
The Blues opened the scoring in the 20th minute through Ramires. They doubled their lead on the stroke of halftime when Daniel Georgievski scored an own goal before Ramires and Frank Lampard sealed Chelsea's victory after the break.
Atletico Madrid moved on to six points as second-half goals from Diego Godin and Arda Turan helped the Spanish side to a 2-1 win at Porto in Group G.
Dortmund was in a different class to Marseille and took the lead when Lewandowski ended a counter-attack with a clinical finish in the 19th minute. As Dortmund coach Juergen Klopp watched from the stands after being banned for one match, the tall striker then converted a penalty in 80th. Marco Reus was also on the score sheet as Marseille slipped to its second consecutive defeat.
At the Emirates, Mesut Ozil again proved to be an excellent signing for Arsene Wenger's team as the Gunners took command of the group, three points clear at the top ahead of Dortmund's visit later this month.
Ozil sidefooted into the net in the eighth minute after Olivier Giroud chested down the ball and flicked it on to Aaron Ramsey, who delivered the cross that the playmaker met.
Ozil then assisted Giroud, pulling back the ball for the former Montpellier forward to score in the 15th minute.
In a game short of chances, Barcelona had to wait until the 75th minute to avoid another frustrating night in Glasgow, having slumped to a shock defeat to Celtic in the group stage last season.
The Spanish giants capitalised on the sending-off of Celtic captain Scott Brown, who was given a straight red card in the 59th minute for kicking out at Neymar. Celtic's overworked defence failed to hold out for the final half hour as Fabregas headed a cross by substitute Alexis Sanchez into the corner, earning Barcelona a second straight victory in Group H after beating Ajax 4-0.
In Porto, Turan scored the winner four minutes from time as Atletico Madrid rallied to secure a 2-1 win.
The result sent the Spanish club to the top of Group G, three points clear of Porto. Zenit St Petersburg and Austria Vienna drew 0-0 in the other group game and have one point each.
Atletico is unbeaten this season and defeated Real Madrid in the Spanish league last weekend.
- AP