An injury-time header from defender Sami Hyypia - greeted with relief, tinged with a fair amount of embarrassment - finally saw off Wolves,whose last away win in the top flight was 20 years ago in the old First Division.
'Don't moan please, we've won,' pleaded the Liverpool manager at the post-match press conference. Houllier should print T-shirts with that phrase: it sums up perfectly the present attitude of the club and their increasingly disillusioned support.
Houllier's reign may well extend beyond this, his latest annus horribilis , and Liverpool may find their Holy Grail of Champions League football, but the Frenchman is an intelligent enough football man to appreciate that three Premiership victories in nine outings, two at home last week against relegation candidates Portsmouth and Wolves, are hardly going to catapult the club back among English football's elite.
Liverpool may have been by far the better side, they may have been denied a strong penalty appeal for Jody Craddock's trip on Emile Heskey, and the goal may have been thoroughly warranted, but a gap of 19 points behind Chelsea and second place in the Premiership, let alone first, is the story of their season.
'Don't ask me about the penalty because I'll get very angry,' said Houllier of the 25th-minute incident, ignored by referee Rob Styles, that might have cost his team victory. 'I just hope it was an honest mistake, that's what I told him. He was too far away to see properly. I don't think it's players who get you the sack, it's referees. How many decisions of that calibre have we had this season? It's incredible.'
David Jones, Wolverhampton's manager, saw an entirely different game but also felt aggrieved for a failed penalty claim - this one early in the second half after a supposed push by Igor Biscan on Ioan Ganea.
'I've just seen theirs - it's not a penalty,' said Jones. 'He [Heskey] has gone down like a sack of spuds. If he had finished it, it would have been in the back of the net. Instead, he waited and invited the tackle. Do I think ours was a penalty? Of course it was!'
At least those appeals offered some talking point in a game that, as Houllier's opening gambit hinted, lacked any quality to talk about until the second of three added minutes of stoppage time. Steven Gerrard's left-flank corner was met by an athletic leap from Hyypia, rising above Paul Butler to deposit the ball in the back of Paul Jones' goal.
There was a bit of long-range shooting, a Michael Owen run and shot late in the first half, a fine diving stop from Jerzy Dudek early in the second half, and plenty of late Liverpool set-piece pressure. But neither the gale-force conditions - nor two thoroughly mediocre teams - were going to allow this to be a classic.
'We will keep digging in and keep going,' said Jones of Wolves' increasingly desperate predicament. 'The performance we've put in came from all our hard work - it's just the result that's frustrating for us.' And that, as Houllier will testify, is all that matters.