*Late Dortmund goal ruins Wenger's night at The Emirates
* Polish striker Lewandowski gives visitors 2-1 victory
* Ends Arsenal's long unbeaten run in all competitions
Birthday greetings? Bottle of wine? The Beatles classic had a hollow ring for Arsenal manager Arsene Wenger on Tuesday as Borussia Dortmund handed out a Champions League reality check on the day he turned 64.
Robert Lewandowski's late volleyed winner earned Dortmund a 2-1 victory at a rain-soaked Emirates Stadium to throw Group F wide open just when Arsenal seemed capable of cruising through to the last 16 from a formidable section.
Without reproducing the scintillating form of recent weeks Arsenal were set for a point after Olivier Giroud cancelled out Henrikh Mkhitaryan's opener just before halftime but Lewandowski's composed 82nd minute strike condemned Arsenal to a third home defeat in a row against German opposition.
It ended a 12-match unbeaten run in all competitions for the Londoners and left Wenger's side tied on six points with last year's European Cup runners-up Dortmund and Napoli and a daunting looking away game to come in Germany in two weeks.
"We were not as good as we can be offensively and some of the players tonight were not as fresh as recently," Wenger told reporters. "If you can't win games you mustn't lose them.
"In the second half we were on top but if you concede two goals you can only say we have to look at ourselves at not being mature enough in situations like that.
"It's tight now and difficult for us. But possible," added Wenger whose side will need points from their away games in Dortmund and Napoli to reach the knockout rounds.
Wenger was tearing his hair out after both Dortmund goals and he even got some sympathy from Dortmund coach Juergen Klopp, who watched the match from the stands as he completed a two-match UEFA ban for his rant during their defeat by Napoli.
"I'm sorry, really!" he said when asked if he felt bad about ruining Wenger's birthday.
"It's a problem with the date. My birthday is in June when there are no football matches and I'm always on holiday."
Widely praised for their free-flowing football against Norwich City at the weekend, Arsenal appeared to be basking in their own hype as Dortmund, beaten by Bayern Munich in last year's final, bossed the opening 20 minutes.
Marco Reus had already fired one dangerous effort wide before the visitors went ahead in the 16th minute.
Midfielder Aaron Ramsey, who has hardly put a foot wrong in a barnstorming start to the season, was caught in possession by Lewandowski on the edge of his own penalty area and the Pole played a quick pass to Armenian Mkhitaryan whose low shot nestled in the corner of Wojciech Szczesny's net.
Arsenal were nearly given an immediate reprieve when Mats Hummels felled Giroud inches outside the area and escaped with a booking. The resultant free-kick came to nothing.
Dortmund's yellow army of fans drowned out the home support for much of the half but Arsenal finally stirred with Jack Wilshere denied by keeper Roman Weidenfeller after being sent clear by Tomas Rosicky before the latter had a shot cleared off the line by Hummels.
Arsenal's only real fluent spell of the match earned a reward four minutes before halftime when Weidenfeller and Hummels got in each other's way trying to deal with Bacary Sagna's cross and Giroud thumped the loose ball into an empty net for his seventh goal of the season.
Dortmund began the second half apparently intent on stifling Arsenal's momentum with a passage of "keep ball" in harmless areas of the pitch but it had the desired effect with Arsenal becalmed until the introduction of midfielder Santi Cazorla.
The Spaniard, replacing Wilshere who was feeling the effects of an early tackle on his ankle, injected energy into the hosts and he curled a long-range shot against the angle of post and crossbar after being teed up by an otherwise quiet Mesut Ozil.
A draw would have suited Arsenal and kept them in control of the group but an unmarked Lewandowski provided a painful sting in the tail from Kevin Grosskreutz's cross to bring the Gunners down to earth after their charge to the Premier League summit.
It was a bitter blow for the hosts, especially with Lewandowski perhaps lucky to escape punishment for a possible elbow on Laurent Koscielny, but the perfect fillip for Klopp who will be back at pitch-side for the return in two weeks.
"I don't think it was a red card," said Klopp. "It was one of many one-to-one battles they had all night.
"You can say that we only had three shots on goal and scored twice but we were strong and it's the result that matters. We are back on track now."