Two goals from Luis García and Steven Gerrard's first in 16 games this season were enough to secure Liverpool's passage to the last 16 of the Champions League with two games to spare after PSV Eindhoven overcame Galatasaray 2-0 in the Netherlands.
Benítez was never going to criticise Noel White publicly for his damning comments about the manager that prompted his resignation from the Liverpool board yesterday. He is far too decent for that. Instead, he responded in the only way he knows how, with actions, and while the scoreline did not tell the whole truth of a game that had hung in the balance before Fernando Menegazzo, Bordeaux's Brazilian midfield player, was sent off for a disgraceful head-butt in the 67th minute, Benítez can seldom have taken as much satisfaction from a result.
There is something of the Frank Sinatra about Benítez. The Spaniard likes to do things his way and on his terms, even if his laid-back manner smacks of a man who is happy to take orders from others.
Whether it was intended as a comeback at White, or the critics who have condemned his compulsion to tinker, only Benítez will know, but his decision to stick with the team that defeated Aston Villa 3-1 in the Barclays Premiership at the weekend rather than ring the changes for the 100th consecutive game still registered as a Hallowe'en shock. That it paid off handsomely, however, is unlikely to prevent the manager from changing things at home to Reading on Saturday.
Benítez had claimed that Bordeaux were “more comfortable” playing away from home, but while the statistics did not suggest as much — they had not won on their travels since mid-August, the French side made a decent fist of it until Menegazzo's moment of madness undermined their efforts.
Reacting when John Arne Riise refused to throw the ball back to the French side after they had kicked it out for a player to be treated for injury, Menegazzo head-butted the defender in full view of Markus Merk, the referee, and was promptly given his marching orders as the Norwegian was left with a badly bloodied left eye.
It was a shame because Bordeaux had refused to fade into the shadows after García's third goal of the season gave Liverpool a 23rd-minute lead.
Dirk Kuyt collected a throw-in from Steve Finnan and dribbled close to the right byline before checking his run and laying the ball off for Gerrard. Spotting that García had stolen a yard on his marker, Gerrard floated a perfectly weighted cross to the far post that the Spaniard thrashed into the corner on the volley.
The hesitancy that had plagued Liverpool in France a fortnight earlier was still evident early in the second half, even if the influential Gerrard was doing his best to jolt the hosts from their inertia.
Florian Marange was allowed time to cut inside from the left and fizz a swerving 30-yard drive towards goal that José Manuel Reina did well to tip over before Bordeaux threatened again three minutes later.
Riise sold Xabi Alonso short in the centre circle with an under-hit pass that forced the Spaniard to squander possession, from which Pierre Ducasse launched a fine counter-attack. Julien Faubert darted forward before slipping the ball through to Jean-Claude Darcheville as Jamie Carragher frantically back-pedalled, but the former Nottingham Forest striker shot straight at Reina.
Liverpool were riding their luck, much as they had done at the Stade Chaban-Delmas, so it was inexplicable when Menegazzo reacted as he did and as soon as he departed, Ricardo Gomes's side wilted.
Gerrard had been Liverpool's one guiding light so it was fitting that the captain should score the goal that settled the match 18 minutes from time.
Whatever Gerrard's dissatisfaction with his role on the right, few can question his appetite and having miscued two inviting chances moments earlier, the England midfield player made no mistake when released by Boudewijn Zenden.
The goal sapped Bordeaux of what little life they had left. García caught David Jemmali in possession four minutes later and slotted a cool finish beyond Ulrich Ramé.
Sami Hyypia should have added some gloss to the scoreline late on but headed over from six yards out, but, by then, Benítez, the silent assassin, was already smiling.
