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Chelsea players Fernando Torres and Eden Hazard celebrate a goal against Schalke in the Champions League. Reuters

Arsenal don't like playing German teams at home. Borussia Dortmund came to the Emirates, and snatched a winner against the run of play, to make it the third side from Germany to beat the Gunners in the space of a year in the Champions League.

Goals from Henrikh Mkhitaryan and Robert Lewandowski consigned Arsenal to a 2-1 loss, with the home side's lone goal coming from Olivier Giroud.

Chelsea brought out the style in the Champions League with an authoritative 3-0 win over Schalke, Arsenal's conquerors a year ago, with Fernando Torres bagging a brace and Eden Hazard adding the icing.

The other big game of the night at the San Siro ended 1-1 with Milan holding Barcelona to a point. The Italian side now have three draws from three games, while Barcelona saw their 100 percent record in the Champions League come to an end.

At the Emirates, there was no from-another-galaxy start from Arsenal this time around, as Dortmund's high-pressing game caused the home side quite a few problems.

Dortmund were in fact much the better side for the first 25 minutes or so, making full use of the space on the wings left by Arsenal's inside playmakers.

Fullbacks Marcel Schmelzer, on the left, and Kevin Grosskreutz, on the right, were constantly bombing down the wide positions, leaving Arsenal's fullbacks outnumbered.

However, despite Dortmund's bright start, Wojciech Szczesny wasn't exactly too troubled in goal, even if Marco Reus and Robert Lewandowski took a couple of early potshots.

Arsenal were just not able to get into the game really, with Mesut Ozil barely seeing the ball, while Aaron Ramsey and Jack Wilshere also struggled to stamp their authority in the game, with the home side perhaps guilty of just giving Dortmund a little too much respect.

Arsenal's best players of the half, going forward, were Tomas Rosicky, playing for the first time against his former club, and Giroud. However, it was Dortmund that were in control, with the bright start from the away team keeping the Emirates crowd pretty quiet.

It was crucial for Dortmund to take advantage of the early control and that opening goal did come in the 16th minute. Ramsey, of all people, tried to dribble his way out of a crowd just outside his own box, and was caught. Lewandowski then gave the ball to Mkhitaryan, who made no mistake in slotting it past Szczesny.

Arsenal needed to wake up after the goal, and they did, as the first half wore on. Bacary Sagna had a couple of decent opportunities to put in a couple of good crosses, but failed miserably, while Giroud was having the better of Mats Hummels, constantly putting the Dortmund defender under pressure, and even inducing a bad challenge which led to a yellow card.

The Gunners thought they had got their equaliser seven minutes before halftime, when Tomas Rosicky, after some good work from Giroud, struck a sweet volley with his left foot. The strike beat goalkeeper Roman Weidenfeller, but Hummels, who somehow found himself on the line, cleared brilliantly.

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Arsenal striker Olivier Giroud celebrates his goal against Borussia Dortmund with Aaron Ramsey. Reuters

However, Arsenal would get their goal a couple of minutes later. Ramsey found Sagna on the right, with the rightback this time playing in a perfect cross into the six-yard box. Neven Subotic, not knowing his keeper was coming for the ball, and under pressure from Giroud, could only deflect his weak clearance onto Weidenfeller with the ball then falling perfectly for Giroud to thump into an empty net from two yards.

Arsenal had the much better chances in the second half, even if Dortmund started the period better. The home side just looked more dangerous in front of goal, especially when they upped the tempo, with Santi Cazorla, in for Wilshere early in the second half, making a big impact.

The Gunners also put the ball in the back of the net just after the hour courtesy Ramsey, but the referee blew the whistle for a push inside the box, even if replays suggested it was Hummels who had pushed on the back of his own teammate.

Cazorla, then, nearly did make it 2-1, but his delightful first-time strike skimmed off the top of the crossbar.

Arsenal looked in complete control in the later stages of the second half, but Dortmund, with their quality, struck the crucial winner against the run of play off a quick counterattack.

Borussia Dortmund players celebrate their win over Arsenal in the Champions League. Reuters

Grosskreutz, who had made a hash of one cross after another throughout the game, finally got one right, picking out the onrushing Lewandowski at the far post perfectly, with the Polish striker, who was lucky to stay on the pitch after a rather unnecessary elbow on Laurent Koscielny, calmly slotting it home on the volley.

The other game of Group F ended in Napoli's favour, with the Italian side beating Marseille 2-1, which leaves Arsenal, Dortmund and Napoli all on six points after three games each.

At the San Siro, Robinho opened the scoring for Milan in the ninth minute. The Brazilian latched onto a long pass after Barcelona defenders Gerard Pique and Javier Mascherano failed to deal with it, before playing a one-two with Kaka to slot in.

Lionel Messi, who else, equalised for Barcelona, neatly taking in a pass in a crowded penalty area before easily passing it into the back of the net.

Barca dominated possession in the second half, but could not find a way through as both sides settled for a point.

Celtic picked up a vital 2-1 win against Ajax in Glasgow, keeping the Scottish sid every much in the running in Group H.

In Germany, Fernando Torres scored the only goal of the first half for Chelsea. Frank Lampard's cross was headed on by Branislav Ivanovic, with Torres then left with an easy task if heading into a virtually empty net at the far post.

Torres then pretty much ended the game as a contest in the 69th minute, easing the ball in after some good work from Oscar. Hazard got his name on the scoresheet three minutes from time, taking a simple pass forward before finding the back of the net.

Chelsea are now equal on points with Schalke, with the other game in Group E between Steaua Bucharest and FC Basel ending 1-1.

Group G saw Atletico Madrid picking up their third win in as many games with a comfortable 3-0 victory over Austria Wien - Diego Costa grabbing another couple of goals. FC Porto, though, suffered a surprise 2-1 loss to Russian side Zenit St. Petersburg.

Results: Group E: Schalke 0-3 Chelsea; Steaua Bucharest 1-1 Basel. Group F: Arsenal 1-2 Borussia Dortmund; Marseille 1-2 Napoli. Group G: Porto 0-1 Zenit; Austria Wien 0-3 Atletico Madrid. Group H: Celtic 2-1 Ajax; Milan 1-1 Barcelona.