The home side got back to winning ways against the below-par Romanians, which failed to test the defense that has irked manager Jose Mourinho in recent matches.
Despite suffering a second defeat to Basel on matchday five, Jose Mourinho's men were already assured of a place in the last 16 and had little trouble in seeing off limited opposition on Wednesday.
Demba Ba's 10th-minute strike from a Willian corner surprisingly proved the only goal as Chelsea demonstrated little desire to move in for the kill thereafter.
Gabriel Iancu spurned a golden opportunity for the visitors three minutes after Ba’s opener, but Steaua was generally kept at bay with a degree of comfort.
In failing to record victory for a 23rd Champions League game in succession, the Romanian outfit set a new record for the longest winless run in the competition.
Its European campaign is finished for another season, while Chelsea will be aware far sterner tests await when the knockout stages commence in the new year.
Veteran Chelsea goalkeeper Mark Schwarzer replaced the rested Petr Cech to become the Champions League’s oldest debutant – and second-oldest player – at the age of 41 years and 66 days.
Mourinho also recalled Ashley Cole for his first club start since November 2, while David Luiz and Oscar returned from injury against a Steaua side missing suspended captain Alexandru Bourceanu.
Luiz and Oscar each went close before Chelsea took the lead.
A right-wing corner from Willian was flicked on by Oscar and Ba bundled the ball home as Daniel Georgievski attempted to clear.
Iancu should have leveled three minutes later, only to drag his shot wide after being put through one-on-one with Schwarzer.
There was little else to concern a dominant home side, which came close to scoring again when Ciprian Tatarusanu made a point-blank save to keep out Branislav Ivanovic's 27th-minute header.
Steaua's Pantelis Kapetanos and Chelsea midfielder Lampard missed the target with long-range efforts prior to the interval, while an ambitious effort from Cole brought a comfortable save from Tatarusanu.
A delightful Willian cross left Ba with a seemingly simple tap-in eight minutes into the second period, but the Senegalese forward clumsily cleared the crossbar with his finish.
Chelsea appeared content to operate at virtual walking pace thereafter, although another opportunity went begging in the 71st minute when Eden Hazard headed over following good work from substitute Andre Schurrle.
While entertainment may have been in short supply as the game meandered toward its conclusion, Mourinho will doubtless have been pleased to see his side keep a clean sheet after conceding three in each of their last two domestic fixtures.