The Brazil midfielder netted either side of an own goal and Frank Lampard added a late fourth as Jose Mourinho's side made amends for the round one loss to Basle and last season's Europa League defeat at the home of the Romanian champions, despite the early departure of striker Fernando Torres with a knee injury.
Torres, who earlier on Tuesday received a Football Association disciplinary reprieve following his altercation with Tottenham defender Jan Vertonghen, started for a third successive game but lasted just 11 minutes before being substituted after failing to shake off a blow to his left knee.
His replacement Samuel Eto'o had a role in the opening goal, weakly helping on Andre Schurrle's cross for Ramires to prod the ball in.
A strong run from Eto'o, following Juan Mata's incisive pass, then saw the hapless Daniel Georgievski divert the ball into his own net to give the visitors a 2-0 half-time lead.
A roof covered the pitch from the incessant torrential rain, but Steaua were struggling to protect themselves from wave after wave of Chelsea attacks.
Ramires, who was excellent throughout, now has three goals in three games after finishing off a flowing move for his second of the night and Chelsea's third and Lampard netted a fourth in stoppage time.
Mata, who hit the post in the second half, fully justified his inclusion and Andre Schurrle was a constant menace, but encountered little resistance from his opposite number Georgievski.
Chelsea next play Schalke twice, the first contest in Gelsenkirchen in three weeks' time, after claiming a second away win of the season.
The first was at Swindon in the Capital One Cup and the Blues will chase another at Norwich in the Premier League on Sunday.