Joe Cole scored the quickest European goal in Liverpool's illustrious history, just 25 seconds in, to earn his place on the scoresheet for the first time since his move from Chelsea, but Cristian Tanase equalised for the Romanians in the 13th minute.
However Liverpool made sure of the win in the second half, with David Ngog scoring either side of a fine strike by substitute Lucas Leiva.
Roy Hodgson left out Fernando Torres and Steven Gerrard from his squad and named a team which had just three survivors from the weekend's goalless draw at Birmingham.
Hodgson's decision, with a huge game at Manchester United on Sunday, was ultimately justified, though, despite a 30-minute period either side of half-time when the match hung in the balance.
Hodgson had stressed prior to the game that Steaua, the 1986 European Cup winners, would provide a tough test, but it took precisely 25 seconds for his words to be disproved.
Octavian Abduran, under pressure from Cole, left his pass back to his goalkeeper woefully short and Cole nipped in to sidefoot a shot past Ciprian Tatarusanu and in off the far post.
Sotirios Kyrgiakos had a downward header from Maxi Rodriguez's corner blocked by Eric Bicfalvi and Jay Spearing fired a long-range shot over as the Reds looked to press home their advantage but a defensive lapse in the 13th minute allowed Steaua to equalise.
Kyrgiakos and Kelly allowed Tanase to nip in between them to collect Bogdan Stancu's through-ball and he neatly chipped over Reina.
The goal gave the visitors the confidence they needed to start knocking the ball around as Liverpool lost their way.
Cole, released down the middle by Spearing, but with no-one in support, had to shoot from distance and that - and subsequent efforts from range from Ryan Babel and Rodriguez - failed to trouble the goalkeeper sufficiently.
It was a sign of the way things were going that when Spearing implored his team-mates to "pick it up" the call was heard all around a half-full Anfield, who responded with an encouraging round of applause.
Abduran's foul on Rodriguez earned him a booking and Liverpool a 25-yard free-kick just before the interval but Paul Konchesky shot well wide.
Cole was Liverpool's most inventive player, although he did not have much competition in that department, and his good work in holding the ball up early in the second half allowed Rodriguez to fire in a shot straight at Tatarusanu.
The Reds were then gifted the chance to go ahead in the 55th minute when Pantelis Kapetanos pulled back Kyrgiakos as he challenged for Rodriguez's corner.
When Ngog stepped up to take the spot-kick - the last one at Anfield was missed by Cole against Trabzonspor - there was an audible groan.
However, the young French striker shrugged off the concerns of the Kop to expertly dispatch the ball into the left-hand corner before wheeling away with a celebration which may have included a gesture towards his doubters.
It was the 21-year-old's fifth goal of the season and fourth in five European games so far.
Raul Meireles almost marked his first start since arriving from Porto last month with a goal as his 30-yard volley was kept out by Tatarusanu's low dive to his right.
Hodgson made his first change of the night when he sent Lucas Leiva on for Babel, moving Cole out to the left and pushing Meireles further forward.
The substitute has an instant impact as he picked up a weak clearance 20 yards out to drive a shot past Tatarusanu with nine minutes to go.
Hodgson was true to his word as he used the latter stages to give experience to youngsters Dani Pacheco and Nathan Eccleston, players who will have an important role to play in this competition.
Ngog fired home his second in injury time to give the scoreline a more convincing appearance.
It was a night when all the manager's decisions proved to be right.
However, making all the right calls at Old Trafford on Sunday will be a much bigger challenge.