It was vital for the Reds to get back on track after back-to-back defeats to Manchester United and Arsenal in the Premier League, which have made their chances of qualifying for next season's Champions League slimmer.
Philippe Coutinho's strike ensured Liverpool evaded a potential banana skin and made it to the last four where they face Aston Villa in 10 days' time, as they look to record an eighth FA Cup triumph.
There was plenty to learn from Liverpool's display, but here are five noticable aspects from the Reds last night:
Their ability to win ugly:
One fault from last season for Liverpool is that we rarely saw them win ugly, but it has been a signature of their FA Cup run, having progressed through every round as favourites by the odd goal on the road. It was always going to be a battle for Liverpool but they were firmly up for a fight last night, and they came up with that moment of quality from 'O Magico'.
Simon Mignolet is a candidate for the club's Player of the Year award:
Who would've thought it midway through the season? But if Liverpool end the season with the FA Cup in the trophy cabinet at the end of May, there should be a lot of people lining up to thank the Belgian for his contribution during this competition, and for last night in particular. At the start of the second half a save from a long-range effort from Tom Cairney was topped by tipping Ben Marshall's header on the post. The quality of the second stop was summed up by the gasps from the away end when 7,000 Liverpool fans watched it again on the big screen.
Encouraging signs from Dejan Lovren:
A lot of fans, and even some in the media, were wondering where the Croatia international had disappeared to after he was overlooked for the defeat to Arsenal in favour of Kolo Toure, but there was marked improvement from Lovren last night - made all the more impressive by the fact that he had to form a new partnership after only a quarter of the game.
A starting XI with flexibility could be the way forward:
With the way the line-up was reported before kick-off, there was some question over whether the side was going to start with a back three they've been playing with recently - or revert to the four. As soon as you saw Glen Johnson operate on the right flank with Jordan Henderson tucking inside, it was evidently a four. But the Reds hardly looked uneasy when the centre-backs split and allowed the full-backs to push on, and there were instances where the midfield had a diamond look about it. A lot of that was down to the first XI selected by the Liverpool manager, which for tactical nerds like myself, was fascinating viewing.
Another game that suggests more firepower is required:
Daniel Sturridge is evidently trying to work his way back to full fitness and there were times when his touch and sharpness just weren't there last night. But the cutting edge factor from Liverpool is missing, and it's hard to rely on a striker who has been out of the side for much of the season.