However, the Gunners only finished runners-up in the group and face a potentially difficult last 16 encounter when the draw is made next Friday after Sevilla scored three second-half goals to beat Slavia Prague.
Arsene Wenger's team completely dominated the first hour of the match but were hanging on to a slender one-goal lead in the closing stages after the Romanian side pulled a goal back against the run of play.
Arsenal's passing was crisp and accurate in the first half as they seemed determined to show they had got Sunday's Middlesbrough aberration out of their system.
In the third minute the lively Theo Walcott ran on to Robin van Persie's exquisite throughball, but the teenager dragged his shot narrowly wide.
The Dutchman made an impressive return to the side following his lengthy lay-off and lasted over an hour before being replaced by Eduardo.
Former Southampton youngster Walcott lifted another shot over the bar before Arsenal took a deserved seventh-minute lead.
Bacary Sagny's cross from the right found Abou Diaby whose first touch was excellent as he found space for himself before lifting the ball into the roof of the net.
Diaby almost scored another goal four minutes later when his deflected effort from the edge of the area was palmed away for a corner by Robinson Zapata.
Arsenal's first-half dominance deserved another goal and they grabbed it three minutes before the break when van Persie slipped the ball through to Niklas Bendtner and the Dane had no problem firing past Zapata.
After the break it was a different story though as Arsenal completely lost their way against a side that is only fourth in the Romanian League, 11 points adrift of runaway leaders CFR Cluj.
After the excellent Zapata had done superbly to race out of his area to tackle Bendtner and then hack the rebound away from van Persie, Steaua pulled a goal back completely out of the blue.
Dorel Zaharia, who had only just come on as a substitute, looped a 69th-minute header over Jens Lehmann, and it was a goal that seemed to dent Arsenal's confidence.
Emmanuel Eboue was forced to hack the ball over his own bar as the revitalised visitors launched another raid as they sensed an unlikely equaliser.
Ovidiu Petre fired a long-range effort narrowly wide with Lehmann beaten, but a disjointed Arsenal side hung on to claim the three points.