It shows how far Liverpool's aspirations have narrowed this season that they cheered Arsenal's half-time lead over Everton when it was read out at the interval here.
These days it matters less that the Premier League leaders are winning and more that the local rivals are not. For Jurgen Klopp and his players, fourth place is the height of their ambition this season and they remain outsiders even for that.
But it's still a possibility after this rather anxious but ultimately deserved victory and for that they have a right shoulder and a right thigh to thank. They may not be enough to completely turn around this season for Liverpool but they turned around this game and for now that feels like more than enough.
With 17 minutes remaining Liverpool did not look winning this game. Darwin Nunez had just seen a goal ruled out by VAR and as Manchester United rallied down the road in the FA Cup at Old Trafford, Sunday's meeting here with the old enemy was starting to feel like one of those behind the sofa occasions for the home support.
But when Trent Alexander-Arnold delivered a free-kick from the left in the 73rd minute, Virgil van Dijk rose to meet it. The defender missed the ball with his head but it cannoned off his shoulder towards goal. Jose Sa saved but when Diogo Jota returned the ball, Van Dijk headed in conventionally and his team were in the lead.
Liverpool beat Wolves 2-0 in their Premier League clash on Wednesday evening
Virgil van Dijk (right) opened the scoring for Liverpool in the 73rd minute of the game
Salah added to their advantage by finding the back of the net in the 77th minute of the game
With Liverpool and their supporters buoyed, Klopp's team came again down the left four minutes later. This time left-back Kostas Tsimikas crossed and Mo Salah diverted the ball in quite intentionally with the fleshy part of his right leg.
It doesn't matter how they go in and certainly it didn't here. With Liverpool's season threatening to dissolve after last week's Real Madrid humbling and the tame league draw at Crystal Palace that followed games like this one have to be won if Liverpool are to retain any hopes of making the Champions League places.
Liverpool were not particularly convincing. They were a little leaden at times. What happened here against Real Madrid has taken a psychological toll and understandably so.
But a recovery, a revival, has to start somewhere and if Liverpool could find something against a United team for whom the season offers no let-up then who knows where it may take them?
During the first half, Liverpool threatened only sporadically and they looked vulnerable at the other end too.
Young midfielder Stefan Bajcetic – a ray of light in the Anfield gloom – had a shot on the turn from a Salah cross in just the third minute. Had it been directed towards either corner it may well have gone in. Instead Sa stooped to gather comfortably.
Darwin Nunez did score for Liverpool in the 65th minute of the game but it was disallowed
Wolves started the game well but they struggled to perform in the second half of the game
Craig Dawson was a standout performer for Wolves on Tuesday and made several key tackles
Then it was Wolves' turn. Improved under their new coach Julen Lopetegui, they are a more confident side, too. Twice early on they threatened as space in the Liverpool penalty box at the Kop end allowed Joao Moutinho to work Alisson in the Liverpool goal and then, from the corner, a Raul Jiminez overhead kick landed on the head of Pablo Sarabia but his effort from six yards did not benefit from sound contact and then ball flew wide.
This, then, was Liverpool in a nutshell. Ambitious but vulnerable. Capable but also flawed.
For a while, nothing much more happened. Liverpool's low confidence was palpable while the home crowd seemed, as heinous as it sounds to say, rather too used to it all. Anfield really was very quiet for long periods.
Improvement did arrive later in the first half and on the back of it Liverpool could and should have scored. Harvey Elliott should have done so with a header from a Darwin Nunez cross and was then denied well by Sa after volleying a Nunez lay-off towards the corner.
Liverpool were the better team in the second half as the Wolves threat receded. Fabinho was lucky to stay on after catching Mario Lemina high with his studs – he was booked – and then Nunez was denied a goal by VAR after Jota was rightly judged to have tripped Max Kilman at the end of his buccaneering run in to the penalty area.
Liverpool youngster Stefan Bajcetic (right) was awarded a yellow card during the game
Jose Sa made a handful of good saves to keep Wolves in the game during the first half
Liverpool XI: Alisson; Alexander-Arnold, Konate, Van Dijk, Tsimikas; Elliott, Fabinho, Bajcetic; Salah, Nunez, Jota.
Substitutes: Kelleher, Milner, Firmino, Henderson, Oxlade-Chamberlain, Gakpo, Robertson, Carvalho, Matip.
Wolves XI: Sa; Semedo, Dawson, Kilman, Bueno; Lemina, Neves; Sarabia, Moutinho, Nunes; Jimenez.
Substitutes: Bentley, Ait-Nouri, Collins, Podence, Neto, Jonny, Costa, Gomes, Traore.
Relief was to arrive for Liverpool, even if it was late. At the end Anfield felt like a different place. That's what goals do.
Speaking after the game, Klopp said: 'This was important. We played the way we needed to play. At times we looked in a rush but we calmed down and increased the pressure.
'I wasn't worried after the VAR goal but the reaction was really good. They were really nice goals and the second one was exceptional. There were lots of positives for us. This sets us up in the best possible way for United.
'They are the team in form but it's a home game. We looked like a unit tonight and we need that again on Sunday. We need to build on this.'
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