Twelve months after they last tasted Champions League victory on foreign soil, and for the first time anywhere away from Anfield this season, Peter Crouch's second-half header enabled Rafael Benitez's team to return to Merseyside with their mission accomplished.
This was hardly a vintage display, however, and Liverpool's success owed as much to the ineptitude of their opponents as to their own performance.
Still, the three points leave Liverpool needing just one more victory to guarantee a place in the last 16 and if, as is now highly likely, they progress to the knockout stages, this forgettable encounter will be nothing more than a footnote as they attempt to bring a sixth European title to Anfield.
Benitez said: "The final score is the most important aspect for me, but the performance of the team was good because the players worked really hard to control the game. Winning away was important for us, especially in the Champions League, but the clean sheet was also a big thing for the team because it will give the players lots of confidence."
Having built a reputation as one of the game's more pragmatic coaches, Benitez sprung a surprise on his Bordeaux counterpart, Ricardo Gomes, by naming an adventurous starting XI with the flair of Luis Garcia and Mark Gonzalez on the flanks of a team already lacking injured captain Steven Gerrard and midfielder Momo Sissoko, whose ankle injury restricted him to a place on the bench.
Perhaps Bordeaux's failure to register a Champions League goal this season had emboldened Benitez, but it was clear from the Spaniard's demeanour in his technical area from virtually the first kick that he was not entirely happy with his defensively-challenged wide players.
Benitez gesticulated frantically at Gonzalez and Garcia as Bordeaux attempted to profit from the unguarded space down both sides of the pitch. The only saving grace for the two wingers was that Bordeaux, in the first half at least, lacked any kind of cutting edge in forwards Lilian Laslandes and Jean-Claude Darchevillie.
Although the pace of Craig Bellamy kept Bordeaux on edge defensively, the home side created the early chances, with playmaker Johan Micoud, in particular, guilty of spurning a golden opportunity to put them ahead.
He was allowed to rise unchallenged by Jamie Carragher and Steve Finnan six yards from goal as a free-kick arrived in the penalty area on 25 minutes, but instead of testing goalkeeper Pepe Reina, the Frenchman failed to connect with the ball as it sailed fractionally past his forehead and wide of the far post.
It was a bad miss, but Crouch went one better nine minutes before the interval when, after springing the offside trap to connect with Bellamy's cross, he aimed a side-foot volley three yards wide of Ulrich Rame's far post. The England forward is nothing if not resilient, though, and he was only denied an opening goal from a similar position moments later when Franck Jurietti's block diverted Crouch's close-range shot into the side-netting.
Bordeaux's Brazilian midfielder Fernando Menegazzo was becoming a growing threat until Crouch made up for his earlier misses by scoring Liverpool's first away goal in the Champions League since last October when he headed Bellamy's corner past Rame on 58 minutes. The corner had been won by Garcia, who showed the first glimpse of his attacking prowess by cutting into the penalty area and testing Rame with a left-foot effort from 12 yards which the goalkeeper could only push behind for a corner.
For a player who stands at 6ft 7in, Crouch's return of headed goals is unimpressive. However, he timed his run to perfection on this occasion as he arrived behind Sami Hyypia at the near post to head the ball down and into the net from six yards. With their Champions League ambitions evaporating, Bordeaux threw caution to the wind in the closing stages but to no avail.