Milan Jovanovic's first-half header was cancelled out when the Reds captain on the night allowed Eder Bonfim's effort to escape his grasp and creep over the line.
A point would have been enough to put Roy Hodgson's side through but Utrecht's 3-3 draw with Napoli ensured they could not be caught at the top of the table with a match still to play.
The Reds boss put his faith in fringe players and reserves having travelled to Romania without eight first-teamers, only three of whom were injured, and he was rewarded by the likes of Jovanovic and Babel.
Neither has made much of an impression to date in their Anfield careers, although Jovanovic admittedly has only had a little more than four months to settle in.
However, they both did a decent enough job on a night when they could easily have gone missing again.
The same could not be said of Joe Cole, returning from a five-week lay-off with a hamstring injury.
Hodgson had admitted before the game the England international was low on confidence after a suspension and injury-interrupted start to his Liverpool career and that showed in his performance.
Despite playing in his supposedly favourite position behind the striker Cole cut a peripheral figure and was unable to affect the game in any way before he was replaced 15 minutes from time by David Ngog.
The opening exchanges were unremarkable except for plenty of non-harmful Steaua possession and Reina, captaining the side in the absence of the injured Steven Gerrard and Jamie Carragher, being targeted by a fan with a laser pen.
It was the second occasion this season the Spain international has had to contend with the irritation, the first coming in their Europa League play-off against Trabzonspor in August.
A complaint to Turkish referee Bulent Yildirim and a stadium announcement thankfully appeared to halt the offender.
By that time, however, Steaua should have been ahead but Eric Bicfalvi headed over left-back Iasmin Latovlevici's cross from eight yards.
It proved to be a costly miss as Liverpool took the lead with their first chance in the 19th minute.
Jovanovic, whose only previous significant contribution since joining in the summer was to score in the ill-fated Carling Cup exit to Northampton, started and finished the move.
The Serbia international, who has been linked with a move back to former club Standard Liege despite only leaving in the summer, worked the ball out to Babel on the right.
When the Dutchman crossed to the far post Jovanovic headed home and celebrated by kissing the badge on his shirt, pointing at the handful of travelling Liverpool fans and then the floor - intimating that he wanted to stay at Anfield.
Babel almost had a hand in creating a second goal but his pass which picked out Cole on the penalty spot was miscontrolled and Dani Pacheco eventually bundled a shot wide from the edge of the area.
But Liverpool had a lucky escape in the dying seconds of the first half when in-form striker Bogdan Stancu, scorer of 12 goals in 17 league appearances, somehow stabbed wide from eight yards when it seemed easier to score.
Early in the second half Reina saved low from Geraldo Alves' header and tipped Stancu's shot, which looped up off Fabio Aurelio, over the crossbar.
The Steaua striker played a significant part without actually touching the ball in the home side's 61st-minute equaliser.
Stancu was positioned in front of Reina - played onside by Danny Wilson - when Eder Bonfim launched his header but the goalkeeper, distracted by his opponent's presence, allowed the ball to squirm out of his grasp, through his legs and over the line.
Sotirios Kyrgiakos powered a header at the crossbar and over from Aurelio's corner as the visitors responded.
But ultimately Liverpool were happy to hang on for a third point in as many Group K away matches, maintaining their unbeaten run in Europe this season, and that was enough to achieve their objective.