The Blues had already qualified for the last 16 prior to the final match of the group campaign against already-eliminated Steaua, yet Jose Mourinho insisted his side were not contenders for the European Cup this term.
Ba's early goal earned victory over the Romanians, but on this evidence - as well as in the defeats to Basle at home and away - there is much to do if the Blues, the 2012 winners, are going to advance to the latter stages of the competition in the new year.
Mourinho and his players were the targets of laser pens from the away end throughout and the Portuguese was at times aghast at the inability of his side to hit the target, either when passing or in front of goal.
The Blues' only goal was initially deemed to be an own goal by Daniel Georgievski before Ba was subsequently confirmed as the scorer.
Ba missed a sitter from six yards early in the second half when found by a Willian cross, leaving Mourinho, who has expressed his frustration as his strikers have struggled to score this season, to shrug his shoulders.
Seven changes were made from the starting line-up following the loss at Stoke, with Ashley Cole returning after a seven-game absence, due to a niggling rib problem and the form of Cesar Azpilicueta.
Mark Schwarzer was given a rare start in goal, becoming the oldest Champions League debutant aged 41, and watched as the early action took place at the opposite end with a series of corners and chances for Chelsea.
David Luiz, like Cole making his first appearance since the November 2 loss at Newcastle, mis-hit a shot from a Willian corner and Oscar then surged forward before firing narrowly wide.
Chelsea took the lead in fortuitous circumstances.
Mourinho had joked that even a training ground dummy would have the good fortune to score against his side from a corner at present, but it was Steaua's defence which was static from a Willian set-piece.
Oscar flicked the ball on to the back post and Georgievski contrived to allow Ba in at the back post to net.
Steaua missed the chance to reply immediately when Gabriel Iancu latched on to a through ball which, worryingly for the hosts, split the Chelsea defence but dragged his shot wide when he should have scored.
Branislav Ivanovic met an Eden Hazard cross and had a header saved at point-blank range by Ciprian Tatarusanu.
Frank Lampard shot over and Cole fired straight at Tatarusanu from long range as Chelsea's dominance continued.
The Blues' corner tally reached double figures before the interval but still their ruthless streak deserted them.
Ba was culpable again when he fired over from six yards out with just Tatarusanu to beat after being found by a good Willian cross.
Mihai Pintilii shot narrowly wide for Steaua but still Schwarzer was little more than a spectator as Chelsea forged forward.
Georgievski cleared a dangerous Hazard cross after Andre Schurrle had replaced Oscar, with Mourinho seeking a spark.
The German nearly produced it, cutting along the byline before Hazard headed over.
Substitute Kevin De Bruyne forced a corner and Ba netted when Steaua failed to clear the set-piece, but from an offside position, as once again Chelsea failed to double their advantage.
Alexandru Chipciu had a shot saved by Schwarzer in the first of four minutes of stoppage time but that was as good as it got for Steaua as Chelsea won unconvincingly to cement their place at the Group E summit.