It has been a season to forget for Liverpool, but they are now just three wins away from making it a finale to remember. Thursday's 4-2 victory against Manchester United means last season's champions are now firmly in the hunt for the top-four finish that had seemed beyond them for so long.

If Jurgen Klopp's team take nine points from their three remaining games -- West Brom (a), Burnley (a) and Crystal Palace (h) -- a place in the top four could come down to goal difference if third-place Leicester take three points from their final two fixtures. If that proves to be the case, Marcus Rashford's miss in the final seconds of stoppage time, when the United forward shot wide when it appeared easier to score, could yet prove decisive.

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In this strangest of Premier League seasons, when a six-game losing streak at Anfield between January and March sent Liverpool plummeting down the table, recent jitters experienced by Leicester and Chelsea, who occupy third and fourth going into the final week of the campaign, have suddenly given Klopp's team the chance to snatch a Champions League place.

Liverpool top the form table over the last 10 league games, so they have quietly rediscovered their ability to get results in recent weeks. That run, and their performance at Old Trafford, only serve to emphasise that they remain a team to be reckoned with and arguably the closest to champions Manchester City when at their best.

But salvaging their season by securing Champions League qualification will feel like a major success following their torturous campaign as defending champions -- a year that has seen them lose key players, notably Virgil van Dijk, to long-term injuries and suffer that historically bad run of home defeats.

Beating second-place United at Old Trafford -- Klopp's first win away to United as Liverpool manager -- will undoubtedly act as a springboard ahead of the crucial final week.

"Great fight, good game, intense -- all derbies should be -- and my first win at Old Trafford," Klopp said. "Good timing I would say. We needed it. We deserved it. All good.

"We are still in the game, in the race. That is all we could have done tonight. It is very intense. We have to recover quickly and go again."

This game, rescheduled after being postponed on May 2 following protests by United supporters opposed to the club's owners, was not all plain sailing for Liverpool, however.

If anything, the 90 minutes showcased the good and bad of both teams, offering a glimpse of why neither were able to mount a consistent challenge to City in the title race.

Liverpool started poorly, with inexperienced central defenders Nat Phillips and Rhys Williams targeted by United in the early stages. When Phillips deflected a Bruno Fernandes shot into his own net on 10 minutes, Klopp's team looked set for a long night and the negative result that would all but end their top-four ambitions.

But United's bright start quickly fizzled out, perhaps because Ole Gunnar Solskjaer's team are already assured of Champions League qualification and also because they have a Europa League final against Villarreal in Gdansk, Poland, to think about on May 26.

Liverpool, on the other hand, had everything to play for and their greater desire showed. But their superior quality was also key.

Klopp's team has under-performed spectacularly at times this season. In many ways, Solskjaer's United squad has over-performed and that was evident as Liverpool exposed the frailties in the home side's armoury.

The hapless Fred was overrun in midfield, while Scott McTominay's limited passing ability also allowed Liverpool to dominate possession and keep United penned in their own half.

And the absence of injured captain Harry Maguire at centre-half showed just how much United rely on the £80 million defender. Without Maguire, United's options are unimpressive, as the error-strewn performance of Victor Lindelof and Eric Bailly highlighted.

But Liverpool still had to take advantage of United's shortcomings. Too often this season, Klopp's players have failed to impose themselves on inferior opponents, so there was no guarantee that this game would be any different.

Yet Liverpool did show up and, after having a penalty ruled out by VAR on 26 minutes after a Bailly challenge on Phillips, they levelled the scores when the impressive Diogo Jota flicked a Phillips shot past United goalkeeper Dean Henderson.

Two goals in the space of three minutes either side of half-time swung the game in Liverpool's favour, when Roberto Firmino scored twice to put his team 3-1 up and in control.

United's inability to control possession or vary their attack -- two issues they must resolve in the summer transfer market -- made it easy for Liverpool to retain the advantage, but a Rashford goal on 68 minutes, following a neat pass by Edinson Cavani, threatened to scupper Liverpool's hopes of a crucial win.

When Phillips cleared off the line from Mason Greenwood two minutes later, Liverpool's mid-season wobble looked to be happening again, but they held out and Mohamed Salah's breakaway goal in the 90th minute put the result beyond doubt.

Liverpool's win heaps the pressure onto Leicester and Chelsea, who meet at Stamford Bridge next Tuesday after contesting the FA Cup Final on Saturday.

Their encounter means one or both will drop points, enabling Liverpool to claim a top four spot if they win their next two games against West Brom or Burnley.

But whatever happens now, the race for the top four will go down to the final day of the season and Liverpool would have grabbed that prospect by both hands had it been offered to them just a couple of weeks ago.