Jose Mourinho's side had already qualified for the last 16 of Europe's elite club competition, but they needed a victory in their final group fixture at Stamford Bridge to guarantee first place.
Ba's first half goal was enough to fulfil that ambition and, while Chelsea were some way from their best, this fairly forgettable encounter could yet prove a significant stepping stone if they go on to have a successful European campaign.
Mourinho claimed on Monday that Chelsea were unlikely to win the Champions League this season because the squad is still a work in progress in the first season of his second spell at the Bridge.
But that sounded suspiciously like kidology from the Chelsea boss in a bid to ease the pressure on his players, who should benefit from a significantly easier draw in the last 16 now they have finished top of their group.
After Saturday's surprise defeat at Stoke, Mourinho opted to rest Petr Cech as one of seven changes to the team beaten by Stoke, with Australian goalkeeper Mark Schwarzer finally making his Champions League debut, while England left-back Ashley Cole returned after a spell on the sidelines.
Schwarzer became the oldest Champions League debutant at 41 years and 66 days, and also the second oldest player ever in the Champions League.
Mourinho was unhappy with his strikers' lack of goals following the Stoke loss, but his criticism sparked an immediate response, albeit against one of the weaker defences Chelsea will face this season.
Oscar came close to opening with barely five minutes played when he ghosted through the Steaua defence and flashed a shot just wide from the edge of the penalty area.
It took Chelsea just 11 minutes to break down Steaua's feeble resistance.
Oscar took advantage of Steaua's sloppy marking and rose to head Willian's corner towards the far post, where Ba got the final touch ahead of Bucharest's Daniel Georgievski, bundling the ball into the net from virtually on the line for just his third goal of the season.
Yet Mourinho had been vexed by Chelsea's careless defending after they conceded six goals in two matches against Sunderland and Stoke last week.
And he was given more reason for concern when Chelsea's defence parted with alarming ease moments after his side took the lead.
Gabriel Iancu surged clear of John Terry and looked odds on to score, only to drag his shot wide with just Schwarzer to beat.
Branislav Ivanovic almost doubled Chelsea's lead midway through the first half, but the Serb's powerful header from Eden Hazard's cross was tipped over by Ciprian Tatarusanu.
Ba should have delivered the knockout blow early in the second half, but he somehow managed to lift his close-range effort well over the bar from Willian's cross.
Steaua's total lack of goal threat ensured Chelsea rarely needed to overly exert themselves in a moribund second period.
Substitute Andre Schurrle injected some life into the closing stages when he jinked into the penalty area and tested Tatarusanu with a low strike.
Tatarusanu could only push the ball back into the six-yard box, but Hazard was unable to capitalise on the rebound as the Belgian headed over.
Ba had a strike ruled out by a debatable offside call in the closing moments, but it was already mission accomplished for Chelsea.