Robin van Persie's late strike sank Steaua Bucharest and gave Arsenal a second successive Champions League win.
Arsenal were far superior to Steaua, but faced frustration until Van Persie fired home Emmanuel Adebayor's pass from 12 yards with 14 minutes left.
Cesc Fabregas missed a good first-half chance for Arsenal, while Kolo Toure headed away Nicolae Dica's goal-bound effort with Manuel Almunia stranded.
Victoras Iacob wasted another opening, but Arsenal deserved their victory.
606: DEBATE
It gives Arsenal the perfect platform for progress out of the group phase as they built on their opening win against Sevilla at The Emirates.
Arsenal survived a scare after six minutes when Valentin Badea headed home, but the goal was correctly ruled out for offside.
The Gunners responded within seconds and should have taken the lead, but Fabregas fired over the top from close range after he was perfectly set up by Alexander Hleb.
Arsenal were in a class above their opponents, but Steaua still posed a threat and Dica fired just wide from 25 yards with Almunia scrambling across his goal in the 19th minute.
Wenger's side almost took the lead in fortuitous fashion six minutes before the interval, but Steaua keeper Robinson Zapata did well to grab Gael Clichy's deflected cross.
Arsenal continued to dominate possession after the break, and keeper Zapata was fortunate to escape when an eccentric dive saw him completely miss Hleb's free-kick but the ball rolled to safety.
Toure showed great defensive awareness to keep Arsenal level after 57 minutes when Almunia's clearance fell to Dica.
He fired a long-range effort towards an unguarded net, but Toure had retreated and headed out of danger.
It was a moment that appeared to shake Arsenal out of their stride, and Steaua went on to enjoy their best spell of the game.
Steaua substitute Iacob wasted a glorious chance to punish Arsenal when he was sent clear after 70 minutes, but he showed a dreadful lack of composure and side-footed a finish high and wide.
Arsenal took advantage of the reprieve to take the lead with 14 minutes left, courtesy of Van Persie.
Adebayor was the creator with a run down the left, and he set up Van Persie to rifle an emphatic finish high past Zapata.
Arsenal manager Arsene Wenger:
"We had to make sure we weren't caught on the counter-attack, and we almost were once but they didn't take their chance and that was the turning point in the game.
"It says a lot about the resolve in the team, not only because we won but because of the focus we have. There is something special in this team and hopefully it will last."
Steaua Bucharest: Zapata, Emeghara, Baciu, Marin, Rada, Petre, Dica, Nicolita, Neaga (Zaharia 77), Surdu (Badoi 85), Badea (Iacob 60).
Subs Not Used: Cernea, Cristocea, Nesu, Croitoru.
Booked: Marin, Rada.
Arsenal: Almunia, Sagna, Toure, Senderos, Clichy, Hleb, Fabregas, Flamini, Eboue (Silva 73), Adebayor, Van Persie.
Subs Not Used: Fabianski, Diaby, Diarra, Denilson, Bendtner, Walcott.
Booked: Adebayor.
Goals: Van Persie 76.
Att: 21,000
Ref: Terje Hauge (Norway).
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