Chelsea needed a win following their shock home defeat by Basle last month and they got the perfect start when Ramires poked in from close-range after Andre Schurrle raced clear down the left and found Samuel Eto'o, who found Ramires.
Steaua almost staggered to half time just one goal behind, but they were dealt a killer blow just before the break when Georgievski capped an awful personal performance with an unlucky own goal, seeing the ball ricochet off him after Eto'o's shot was parried by goalkeeper Ciprian Tatarusanu.
Andre Schurrle, Chelsea's standout player on the night, created the third with a powerful run down the left wing and pass to Oscar, who spotted his compatriot Ramires on the overlap, and the Brazilian finished expertly into the roof of the net.
Chelsea added a fourth in the final minute with another slick counter-attack, this time led by Eto'o. The Cameroonian spotted Willian on the far side, and he rolled it back to Frank Lampard, who drilled in off the post from 20 yards.
On a night when Chelsea could have had six or seven, Jose Mourinho will be satisfied with a convincing display, soured only by a knee injury sustained by Fernando Torres.
PRE-MATCH: Fernando Torres and Juan Mata start for Chelsea. The Spanish striker keeps his place after impressing against Spurs on Saturday, despite picking up a red card late on. Juan Mata starts in Eden Hazard's absence.
19' - GOAL: Steaua 0-1 Chelsea - The Blues lead after a pacy counter-attack. Ramires starts the move with a ball wide to Schurrle. The German crosses for Eto'o, who flicks it on to Ramires to poke in from close range.
44' - GOAL: Steaua 0-2 Chelsea - Chelsea have a deserved second, albeit in fortuitous circumstances. Steaua again caught short at the back as Eto'o drives at goal. The Cameroonian's shot is saved, but richochets off Georgievski and into his own net.
55' - GOAL: Steaua 0-3 Chelsea - Ramires rifles into the roof of the net to put the game beyond Steaua. Schurrle creates it with another brilliant run down the left. He finds Oscar, who feeds Ramires, who finishes.
57' - OFF THE POST! Chelsea turning on the style now as a brilliant interchange of quick passes allows Oscar to play in Mata, whose shot crashes back off the base of the post.
90' - GOAL: Steaua 0-4 Chelsea - Lampard rounds off the win with a trademark 20-yard strike after Eto'o burst forward on the break and picked out Willian.
Possession - Steaua 43% Chelsea 57%
Before this match, Chelsea had only won two of their previous 10 away games in the Champions League.
No Romanian side has ever scored more than one goal against English opposition in the Champions League.
Who should start in attack for Chelsea? With Fernando Torres suspended in the Premier League and now injured, should Jose Mourinho turn to Samuel Eto'o? Or is Demba Ba worth bringing in from the cold? Mourinho has a dilemma.
MAN OF THE MATCH
Andre Schurrle (Chelsea) - Couldn't get on the score sheet but was Chelsea's standout player, playing a key role in two of the four goals. Tore Georgievski to shreds.
Steaua: Tatarusanu 6, Georgievski 4, Szukala 5, Gardos 5, Latovlevici 5, Filip 6, Tanase 7, Stanciu 7, Piovaccari 6, Bourceanu 6, Popa 5. Subs: Tatu 6, Varela 6, Kapetanos 6.
Chelsea: Cech 6, Ivanovic 7, Cole 6, Terry 7, Luiz 7, Ramires 8, Lampard 7, Torres 6, Mata 8, Oscar 8, Schurrle 9. Subs: Willian 7, Azpilicueta 6, Eto'o 8.
THE MATCH IN A TWEET