An early goal from Demba Ba set the tone for the rest of the game, as a much-changed Blues side kept their fourth clean sheet of the Champions League campaign.
The game lacked intensity and a real premium of clear-cut chances, but Jose Mourinho won't mind, as he avoids the likes of Real Madrid and Barcelona in the next round.
Steaua go crashing out of the group stage without a win, and it will be a case of "better luck next year" for Laurentiu Reghecampf's men.
Here are some points of the game that we can take a look at after Chelsea sealed their progress at Stamford Bridge.
*All statistics, unless stated, are provided by WhoScored.com.
So Jose Mourinho finally got the victory he desired after the defeat against Basel two weeks ago, but did he get the performance?
Of course, Chelsea dominated proceedings with 69 per cent possession and generally looked comfortable on the ball. Willian and Eden Hazard showed some nice touches, while Frank Lampard and John Obi Mikel pulled the strings in the midfield.
But again, there was that certain lack of quality on show, that one moment that could have put the game beyond doubt.
Considering the goal came from a set piece, Chelsea's five shots on target from 18 in total highlighted their profligacy in front of goal.
Demba Ba might have claimed the first goal, but his miss from six yards could have been costly for the Blues, with Schalke winning 2-0 against FC Basel.
A clean sheet is of course a bonus, and with just three goals conceded in the six group games, Chelsea have the best defence in the competition.
Nevertheless, having criticised his team's lack of killer instinct in the loss to Stoke, reported by the Guardian's Sachin Nakrani, the evidence suggests that Mourinho has every right to be unhappy with the attackers in the squad at present.
Some might have predicted that a £30 million Brazilian playmaker who speaks little English and has spent the last five years of his career in Russia and Ukraine might struggle to adapt at a club like Chelsea.
But Willian has really proved to be a sensible acquisition since joining from Anzhi Makhachkala.
What was Tottenham's loss has very much been Chelsea's gain, with the 25-year-old showing once again his natural ability on and off the ball.
Starting on the right-hand side, he linked up brilliantly with Branislav Ivanovic, and his energy and desire to create chances for Chelsea made him one of the standout performers, along with Eden Hazard.
He may not start every game, granted, but the former Shakhtar midfielder has displayed the kind of performance the West London club need from their star players, and that will be important in the coming months of the season.
Worrying times are not too far ahead for Steaua Bucharest after another defeat left them winless for the 22nd consecutive game in the Champions League.
The performance itself in the 1-0 defeat to their tactically superior opponents Chelsea wasn't so bad. Rather, it was the lack of a goal threat which made it so easy for the Blues to protect their one-goal advantage.
Federico Piovaccari only came on as a substitute late in the second half, and he struggled to make any sort of impact, while Daniel Stanciu missed a glorious opportunity in the first half to equalise.
Draws against Schalke and Basel would have given them some encouragement ahead of the 2014-15 campaign, although the path to the group stage may be one step too far next time around.
A player with such skill, pace and raw ability, and he's still only 22 years of age, too. It's no wonder why the likes of Frank Lampard praised Eden Hazard so highly in recent weeks, per Sky Sports.
The Belgian winger was signed from Lille 18 months ago in a £32 million deal and, aside from a few minor hiccups, has looked every part of the making of a world-class player.
Mourinho took his time to evaluate how to treat the pacey midfielder, given Hazard's controversial decision to travel to Lille without permission, only to then forget his passport, according to Jack de Menezes of The Independent.
But encouraging Hazard to play with his natural confidence allows him to humiliate defenders and create chances for his teammates, like he did against Sunderland, Stoke and now Steaua.
Another assured performance from the tricky winger, and Mourinho will be hoping there is plenty more to come from a player who has seven goals and four assists so far this season.
Having faced them four times in the calendar year of 2013, Daniel Georgievski will be relieved to see the back of Chelsea after Steaua crashed out of the Champions League.
In those four games, the Macedonian international, who is part Australian, has endured a nightmare for his club.
He scored an own goal in the 4-0 drubbing handed to them by Chelsea back in October and could arguably be credited with another in Wednesday's game after deflecting Ba's effort into his own net.
By all means, Georgievski could just be unfortunate. But he seems to lack the same sort of composure as his teammates, and that is a concern.
Another night to forget for the 25-year-old, but hopefully he can use this as a base to improve for next season's European campaign.
The hype surrounding Fernando Torres' apparent resurgence appeared to have no real foundation to it, with the Spaniard failing to maintain his impressive form after a spell out injured.
In his absence, Samuel Eto'o was the obvious replacement and scored four goals in as many games. But one striker who was not expected to have much of an opportunity was Demba Ba, who scored the only goal as Chelsea beat Steaua Bucharest 1-0.
The Senegalese forward has looked off the pace at times and has only scored three Premier League goals since joining the club in January, but has shown signs of improving his all-round game in recent weeks.
Of course, the 28-year-old missed a simple tap-in from six yards out after a superb delivery from Willian, but it didn't disguise the fact that Ba, among others, is beginning to show signs of development under Mourinho.