Fellow Serie A sides Atalanta and Lazio also won, while Portugal's Vitoria Guimaraes began their match against Salzburg with not a single European player on the team.
Earlier, the match was delayed by one-hour due to the enormous band of Cologne supporters who travelled - many thousands in excess of the official allocation of 3,000 - and the intense atmosphere was created inside the ground.
Arsenal come into this game having started the Premier League season poorly after claiming just six points from the opening four games.
Cologne coach Peter Stoger refused to be questioned on the actions of the club's supporters: "I have no comment about the fans", he said.
Arsenal supporter, and ITV's political editor, Robert Peston tweeted: "These Cologne fans are a disgrace".
"Arsenal have lost their last five at Stamford Bridge in the PL although they did beat the champions in both the FA Cup Final and Community Shield, albeit on penalties, in recent months", Owen wrote on Betvictor.com.
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But he called attention to the suffering Mexico has endured, and called for prayer for that country. The Holy Father noted that he had touched on this topic numerous times.
Cologne fans, who had been singing before kick-off, had even more reason to celebrate when Jhon Cordoba's 40-yard strike gave the visitors a ninth-minute lead.
"In the second half I believe our team was better balanced better equipped going forward".
"Was it the fact that they scored the goal and we didn't know how to deal with it?"
"I think in the second half, he became alive". With the Europa League providing an alternative route into the Champions League, it will be interesting to see how well Arsenal kick off their campaign. "But Sanchez is Sanchez, he is an exceptional football player", Wenger said.
"On the injury front we have no big problems", the Frenchman said.
"Not everyone likes their carnival-style of chants - it's a regional thing that you either like or dislike".
"I think the best way to do it is through the Premier League", Wenger told a news conference before Arsenal host Cologne in their Europa League opener on Thursday.