The Senegalese striker reacted fastest at the back post to tap home from a flick from Oscar, and Chelsea did enough to hold on to the advantage for the remainder of the match.
Ba's goal also helped Chelsea finish in first position in Group E, with Schalke 04 securing second with a win over Basel in Germany.
Here, Sports Mole analyses the game to see if Chelsea were deserving of the three points.
On target 5
On target 2
Was the result fair?
The statistics sometimes lie, but on this occasion, they don't. Chelsea thoroughly deserved the three points, despite failing to extend their advantage after Demba Ba's opener. Bucuresti should have scored after 13 minutes, but after Gabriel Iancu squandered that opportunity, the Romanian side were left to try their luck from distance, ensuring that Mark Schwarzer had a comfortable night on his Champions League debut.
Chelsea's display wouldn't have completely satisfied manager Jose Mourinho, but the Portuguese coach would have been delighted with his side's clean sheet after failing to prevent the opposition from scoring in their last four matches. Eden Hazard and Frank Lampard performed well in midfield, but other than that, it was an effective team performance from the Blues, who will be happy to finish the group in top spot.
Steaua Bucuresti's performance
Steaua Bucuresti weren't expected to cause a surprise at Stamford Bridge, but they impressed with a solid outing in England. Iancu's opportunity after 13 minutes could have changed the course of the match, but after that miss, they only appeared in Chelsea's final third on a few occasions. On a positive note, it was a much more accomplished display than they produced in Romania at the start of the campaign.
Sports Mole's man of the match
Eden Hazard: Hazard's final delivery was lacking in this match, but he was one of the few Chelsea players to attempt to grab the game by the scruff of the neck. He added some much-needed urgency to his team's attack in the second half, and although he missed a six-yard header, he constantly provided a threat on Bucuresti's goal.
It didn't prove costly in the end, but Ba and Hazard both missed attempts in the six-yard box to put the game to bed. With the goal at their mercy, no excuse can be offered for either mistake, but fortunately, it didn't cost their side against Bucuresti.
Gianluca Rocchi had an average game at Stamford Bridge, but his performance didn't change the course of the match. He harshly booked Branislav Ivanovic and Daniel Georgievski for innocuous challenges, while he also blew up a few seconds early at the end of the first half.
Chelsea: Chelsea host Crystal Palace on Saturday as they look to recover from last week's defeat to Stoke City, before they face Sunderland in the quarter-finals of the Capital One Cup.
Steaua Bucuresti: Bucuresti's participation in Europe is over for another season, and they must return home to try to improve on their third position in their domestic league.