Following another quick move with Juan Mata, Schurrle found himself in a good position but dragged his shot over the bar from the edge of the box in the 27th. Mata forced Tatarusanu into a save after a one-two with Eto'o.
The in-form Schurrle created another chance in the 35th as Chelsea gradually took control of the game but his cross just outside the area was squandered by Oscar, who completely missed his left-footed shot.
Steaua tried to set up a faster tempo before halftime but Chelsea used another counterattack to double its lead in the 45th minute. Defender Georgievski, running back toward his goal, could not prevent the ball from ricocheting off him and into the net after Tatarusanu had parried away Eto'o's effort.
Chelsea, which had lost the opening game in the competition group stage for the first time, continued to dominate after the break. Eto'o and Lampard missed good opportunities before Ramires fired home his second goal of the night from Oscar's pass following another move ignited on the left flank by Schurrle in the 55th minute.
Mata then hit the woodwork before Chelsea goalkeeper Petr Cech hit the post with his back after tipping Cristian Tanase's lob over the bar in the 59th minute.
Schurrle had a chance to cap his excellent display with a goal in the 70th but his curled shot at the far corner ended just wide. Lampard completed the rout in the 90th minute with a low shot from the edge of the box after being set up by Willian.