Arsenal manager Wenger turned 64 on the day of the game but Lewandowski played the party pooper as he netted a 82nd-minute winner at the Emirates Stadium to shatter Arsenal's 100 percent record in Group F and end their 12-match unbeaten run in all competitions.
The Gunners trailed to Henrikh Mkhitaryan's early strike, but France striker Olivier Giroud equalised before half-time. However, Poland's Lewandowski had the final word with a typically predatory finish that underlined why he is one of the most coveted strikers in the world.
Dortmund's win lifted them level with Arsenal and Napoli on six points in a three-way tie at the top of the group heading into their return meeting with the Premier League leaders on November 6. "Dortmund were well organised to stop us from playing and we were not as good as we can be offensively," Wenger said.
"We put ourselves on the back foot with the first goal and were a bit naive with the second. "We have to look at ourselves for not being mature enough in situations like that. If you can't win the game you shouldn't lose it."
Dortmund boss Jurgen Klopp jokingly apologised for ruining Wenger's birthday, saying: "I am sorry about this, really. That is a problem of the date. I have a birthday in June when there are no matches. I'm always on holiday!
"To win here in London of course you need a bit of luck, but we made the difference to get the decisive goal and I think we deserved it."
Back in London for the first time since last season's painful Champions League final defeat against Bayern Munich at Wembley, Klopp's classy side seized control in the early stages with some fluid passing and a high-tempo pressing game that stopped Arsenal establishing any rhythm.
With Mathieu Flamini sidelined due to a concussion sustained in Saturday's 4-1 win over Norwich, Wenger had recalled Aaron Ramsey, but the Welsh midfielder's first significant contribution completely unhinged his team.
When Ramsey took possession on the edge of his own area in the 16th minute, he fatally dwelt too long on the ball instead of making a safety-first clearance and was swiftly tackled by Reus.
Lewandowski seized the loose ball and flicked a pass to Mkhitaryan, who took one touch before driving a low strike past Wojciech Szczesny. To their credit, that setback sparked a strong response from Arsenal and Mats Hummels had to clear Tomas Rosicky's shot off the line.
Arsenal's pressure was rewarded with an equaliser in the 41st minute. Ramsey spread play wide to Bacary Sagna and the French defender whipped over a teasing cross from the right.
Neven Subotic got only the slightest of touches as he slid in to clear, but it was enough to distract Roman Weidenfeller, who had come off his line to claim the cross, and the Dortmund 'keeper allowed the ball to deflect off him into the path of Giroud, leaving him with the simple task of firing into the unguarded net for his seventh goal of the season.
Arsenal remained on top for much of the second half but, with Mesut Ozil relatively subdued in midfield, they lacked the killer pass to break down Dortmund again.
Wenger responded by sending on Santi Cazorla for Jack Wilshere, the England midfielder who looked completely out of sorts in a wide attacking role, and the change almost reaped an instant reward when the Spanish substitute fired a first-time strike onto the crossbar from long-range.
Dortmund were showing signs of losing their cool and Lewandowski escaped with a yellow card after catching Laurent Koscielny with a flailing
elbow. That proved a crucial moment as Lewandowski made the most of his reprieve with eight minutes remaining.
A sweeping Dortmund move exposed Arsenal down the right flank and Kevin Grosskreutz looped over a cross to the far post where Lewandowski, left unmarked in yards of space, powered a superb volley past the exposed Szczesny.