The home side started brightly, and they took the lead on 10 minutes when Demba Ba reacted fastest to a flick from Oscar to prod the ball home from three yards.
The Blues continued to dominate against their Romanian opponents, but despite failing to add a second, they held on to finish two points clear of Schalke 04, who finished in second after they beat Basel.
Read below to see how the action unfolded at Stamford Bridge.
6.48pmWhen the draw was made for the group stages, the general belief was that Chelsea had struck lucky after being drawn alongside Schalke 04, Basel and Steaua Bucuresti. The Blues have secured their passage through to the second round, but surprisingly, they still have work to do if they are to finish in first place in the group!
6.51pmThey will conclude their group campaign in top spot if they defeat Steaua Bucuresti at Stamford Bridge, but after a spell of mixed results from Jose Mourinho's men, the result of tonight's encounter is far from guaranteed.
6.54pmThe team news is already in from Stamford Bridge. Mourinho has made a total of seven changes from the weekend.
6.59pmCHELSEA SUBSTITUTES: Cech, Cahill, Ramires, De Bruyne, Mata, Schurrle, Torres
7.01pmAfter losing to Stoke City at the weekend, Mourinho had hinted that he would make alterations...but seven? That has come as a bit of a surprise. The most notable change is in goal, with Mark Schwarzer coming in to replace Petr Cech. Tonight will also see the return of Brazilian duo David Luiz and Oscar, who have been missing recently through injury.
7.03pmAs well as the likes of Gary Cahill, Ramires, Juan Mata, Andre Schurrle and Fernando Torres dropping to the bench, there's also no place in the 18-man squad for either Cesar Azpilicueta or Samuel Eto'o.
7.04pmTeam news for tonight's visitors will be with you in just a couple of minutes.
7.12pmRemarkably, this is the fourth encounter between these two sides in 2013. After Chelsea edged out the Romanians in the Europa League last season, the Blues put in a much more commanding display at the beginning of this European campaign to thrash Steaua 4-0 away from home.
7.16pmA quick stat for you now. Mark Schwarzer will become the oldest Champions League debutant later this evening, while also becoming the second oldest player in the history of the competition. However, he is no stranger to European football. He featured in Middlesbrough's journey to the UEFA Cup final in 2006, while being a mainstay in the Fulham side that reached the final of the Europa League in 2010.
7.23pmBucuresti arrive at Stamford Bridge with little to play for after earning just three points from five games, but it has been a different story on the domestic front. Steaua are unbeaten in 14 league games this season, although rather surprisingly, they don't sit top of the standings. That honour currently belongs to Astra Giurgiu, but Bucuresti can move level with the leaders if they win their two matches in hand.
7.27pmThe goals have been shared out around the Bucuresti side, with Federico Piovaccari heading the scoring stats with five goals. The 29-year-old is currently on loan from Serie A outfit Sampdoria.
7.30pmPREDICTION! Given that they dominated Bucuresti in Romania, the expectation is that Chelsea will repeat that performance here. I doubt it will be as easy as it was around 10 weeks ago, but the Blues should have far too much for their opponents tonight. Chelsea 3-1
7.34pmIf Chelsea don't win this evening, that will let in either Schalke 04 or Basel to stake a claim for first place. Schalke need a victory to stand any chance of qualification, but Basel will guarantee their progress with a point, which would be enough for first place should Chelsea lose at Stamford Bridge.
7.39pmIf you would like to keep track of the action in Germany, you can do so by clicking here.
7.42pmThe two teams are making their way out to a generous reception at Stamford Bridge. The Chelsea supporters will be expecting a performance from their team tonight.
2 minA common theme in Chelsea's previous two Champions League home fixtures is their lack of pace on the ball in their opponent's half of the pitch. Will it be the same again tonight?
3 minCHANCE! A prolonged period of possession from the hosts earns the first corner of the match. The delivery finds David Luiz at the near post, but he scuffs his effort wide.
4 minSHOT! Chelsea have started this game firmly on the front foot, and after Oscar wins possession around 40 yards out, he drives towards goal before curling a shot marginally wide of the post.
6 minChelsea are peppering Tatarusanu's goal. Hazard and Lampard twice work a short corner to excellent effect, but Lampard's drilled cross just fails to trouble the target on both occasions.
9 minI don't think that Mark Schwarzer has had a touch of the ball yet, which says it all really.
10 minGOAL! Chelsea 1-0 Steaua Bucuresti (Georgievski own goal)
10 minChelsea deservedly take the lead after a rapid start at Stamford Bridge. After two corners came to nothing, the third saw Oscar flick the ball onto the back post, where Demba Ba was waiting to tap home. It's a bit unclear as to who got the final touch, but it appeared to be Bucuresti defender Daniel Georgievski. I will keep you posted.
13 minCHANCE! Out of nowhere, it should be 1-1! Gabriel Iancu was played in behind the Chelsea defence, but with just Schwarzer to beat, he dragged his shot wide.
16 minIt should be noted that Daniel Georgievski also netted an own goal in the reverse fixture between the two teams in Romania. He hasn't had much luck playing against Chelsea!
19 minFrank Lampard's a little fortunate to avoid getting a yellow card for a late challenge on Szukala. I've seen those given.
20 minBOOKING! Lampard might have avoided a booking, but John Obi Mikel hasn't. The Nigerian lost the ball in midfield before cynically pulling the shirt of Iancu.
23 minI think that I may have done Demba Ba a disservice earlier on. On second glance, he appears to have diverted the ball into the net with his shin.
27 minSAVE! Chelsea win their ninth corner in 27 minutes. Once again, the short corner is executed perfectly for Hazard to swing the ball in, and Ivanovic sees a header saved at point-blank range by Tatarusanu.
30 minIt remains goalless in Germany in the game between Schalke 04 and Basel, which leaves Basel in the driving seat as far as second place is concerned.
33 minChelsea are comfortable, but the intensity of their play has subsided a little since the opening 10 minutes. Steaua still look game, but they are chasing shadows in the middle of the pitch.
37 minUEFA have indicated that it will remain an own goal by Georgievski, even though it looks clear that Demba Ba got the final touch. Bizarre. Back on the pitch, Lampard sends a long-range strike a yard over the crossbar.
40 minSHOT! The Chelsea corner count is well into double figures now, and when the most recent set piece is only cleared outside of the penalty area, Ashley Cole drills a low shot from 30 yards towards goal, but it's well claimed by Tatarusanu.
43 minI wish UEFA would make up their mind. They are now saying that the opening goal belongs to Demba Ba. Please, just leave it at that now - that's the correct decision.
8.33pmThe referee blows the half-time whistle two seconds before the 45 minutes is up, but that's your lot for the first half. Chelsea have dominated this from the start, but as long as it remains 1-0, Bucuresti remain in this match.
8.37pmAs you would expect, Chelsea are clear on all of the half-time statistics. They've had 11 shots to Steaua's five, they head the corner count 12-0, while they have had 72% of possession.
8.41pmIt remains 0-0 between Schalke and Basel, but the visitors have been reduced to 10 men after having Ivan Ivanov dismissed for a professional foul on the half-hour mark.
46 minThe two teams are back out at Stamford Bridge. Neither team have made any alterations. Chelsea get us back underway.
48 minBOOKING! That's one of the softest bookings that you are ever likely to see. Ivanovic is handed a yellow card for clipping Latovlevici, but he hardly touched the defender. That could prove costly later on in the competition.
51 minBOOKING! Actually, here is another contender. Cole and Georgievski slide in competitively for a 50-50 challenge, but there is no malice from either player. The Bucuresti defender came off the worst, but he is the one who has been cautioned!
53 minCHANCE! Demba Ba has missed an absolute sitter! Some excellent approach play from Chelsea found Willian on the right, with he Brazilian curling in a low cross to the near post for Ba. However, despite seemingly having the simple task of tapping home, the striker struck the ball over from six yards.
57 minThere has been a goal in Germany - Schalke have taken the lead! The German outfit are aware that only a victory will do this evening, and Draxler has given them the advantage early in the second half.
60 minSome intricate play from Hazard earns Chelsea a free kick on the left-hand side around 40 yards from goal. Oscar curls over the set piece, but it is straight into the hands of Tatarusanu.
62 minSchalke have doubled their lead in Germany. Basel are down to 10 men, so that match could be over and done with.
65 minBucuresti have started to show a bit more ambition in the past five minutes, but they are only sending speculative efforts from long distance towards Schwarzer's goal. Chelsea could do with stepping up the tempo. Bucuresti are still in this game, and a draw won't do.
67 minSUBSTITUTION! Mourinho makes his first change of the match by bringing off Oscar for Andre Schurrle, who scored twice at Stoke City at the weekend.
71 minCHANCE! Hazard has grown into this match the longer it has gone on, and he does superbly to spray the ball out to Schurrle. The German advances into the penalty area, and the ball ricochets back to Hazard, who heads over from close range when he really should have found the net.
73 minChelsea have improved since the arrival of Schurrle but they nearly get caught down the left by Bucuresti. Piovaccari does well to cut inside Cole, but his shot is weak and straight at Schwarzer.
75 minHazard is doing everything that he can to double Chelsea's lead, but nothing has paid off so far. He glides past two defenders to set up an opportunity from 25 yards, but he miscues his shot high into the stand.
78 minBOOKING! Iasmin Latovlevici goes into the book for attempting to pull the hair of Willian. Yup, you read that right.
81 minSUBSTITUTIONS! Mourinho has thrown on Ramires and Kevin de Bruyne for the final 10 minutes. Can Chelsea hold on at Stamford Bridge?
85 minThere's hardly any atmosphere at all inside Stamford Bridge. I'm not sure whether the supporters think that this match is over, or whether it's anxiety, but either way, they need to motivate their team - they are looking very lethargic.
88 minDe Bruyne does well to manouvere his way down the left-hand side, but his cross is bundled behind for a corner. It's quickly cleared by Bucuresti, and when the ball is clipped back into the box, Ba smashes the ball into the top corner, but the flag was up for offside.
90 minWe are into added-on time, but Steaua have their first corner! It's cleared to Chipciu, who drills a low shot at Schwarzer, but the Australian stopper deals with it well.