Former Reds striker Luis Suarez opened the scoring in the first half at Camp Nou, before Lionel Messi added two more goals in the final 15 minutes - including an incredible 30-yard free kick - to put Barca in complete control ahead of this return fixture.
Liverpool have reached successive Champions League semi-finals but they now have it all to do against a team who have won their last two matches at Anfield.
Firmino played the final 11 minutes of the first leg but is struggling with a muscular injury, while Salah was concussed in Saturday's 3-2 league win against Newcastle United and Jurgen Klopp has confirmed he is out of this second leg.
The victory at St James' Park at the weekend ensures that the Premier League title race will go down to the wire. With one match to go - a home meeting with Wolverhampton Wanderers next Sunday - it is looking increasingly likely that all of Klopp's eggs are sitting in one basket.
Liverpool may go into the final game of the season needing a helping hand from elsewhere, though, as Manchester City can regain top spot in the Premier League with victory at home to Leicester City in Monday's match at the Etihad Stadium.
For now, as has been the case for a number of months, Klopp can only take it one game at a time. The midweek visit of Barcelona is now effectively a free hit of sorts, with last week's late collapse in the first leg surely leaving them with too much to do.
Making that five in succession in European competition for the first time since October 1984 is the absolute minimum the Merseyside outfit must achieve on Tuesday, while hoping that their attacking stand-ins - possibly Divock Origi and Xherdan Shaqiri - can help to score the three goals needed at the other end of the field.
One goal for Barca, though, will leave Liverpool needing four goals. Against this Barca side, with 16 league clean sheets to their name this term, that is next to impossible.
Liverpool are unbeaten in 19 home matches in all competitions, only enjoying a longer run once under Klopp - a run of 25 between January 2016 and January 2017 - and that is a record the German will want to keep intact.
In a week that could end with Liverpool finishing another season trophyless, they will at the very least want to give supporters something to be proud of. Pushing Barca all the way without two key men would be a good way to go about doing that.
Recent form in Champions League: WDWWWL
Recent form (all competitions): WWWWLW
Barcelona will not be taking anything for granted when they make the trip to Merseyside, having somehow squandered an identical three-goal lead to crash out at the quarter-final stage against Roma last season.
Roma, who unlike Liverpool had an away goal to their name, took Barca apart in the home leg to produce one of the all-time greatest comebacks.
Liverpool also have their own Champions League highlight reel when it comes to dramatic one-off matches, not least the 2005 final when three goals down against AC Milan with 45 minutes to play.
Yet comebacks of this nature are few and far between, making them all the more special when they do occur.
Barcelona have already won two away Champions League games in England this season, winning 4-2 at Tottenham Hotspur in the group stage and 1-0 at Manchester United in the quarter-finals - no side has ever won three away games in England in a major European competition in a single season.
The Catalan giants have won just five of their last 18 away Champions League knockout ties, meanwhile, but four of those five victories have come in England, with the other against PSG in April 2015.
It has hardly the most inspiring of returns for a club as successful as Barca down the years, yet this is the first time they have made it this far in the competition since lifting the famous trophy in 2015.
With the La Liga title being wrapped up last month with a few matches to spare, and a Copa del Rey final clash with Valencia on the horizon, Ernesto Valverde could become just the third man in the club's proud history to pull off the clean sweep.
Given that Valverde also had the luxury of resting players for Saturday's dead-rubber league clash with Celta Vigo, which ended in a 2-0 loss to end his side's five-match winning run, Liverpool will come up against a Barca side feeling fresh and ready to bury the demons of recent campaigns.
After three disappointing European campaigns in a row, Barcelona appear to have finally found their way again on the big stage.
Recent form in Champions League: DDWWWW
Recent form (all competitions): WWWWL
Klopp likely would have named a full-strength side on Tuesday, even though the tie looks to be as good as over, but his hand has been forced somewhat by the injuries to Firmino and now Salah.
Daniel Sturridge has been tasked with filling in through the middle, but Klopp may opt to go with Origi for this match given his late goal against Newcastle, which was set up by Shaqiri - the favourite to replace Salah on the right.
There is another major absentee in midfield, too, as the injury picked up by Keita in the first leg has ruled him out of the remaining games of the season. Jordan Henderson took over at Camp Nou, got the nod at St James' Park and should retain his spot here.
As for Barcelona, they will be without left-sided forward Ousmane Dembele for this trip to Anfield as the Frenchman has sustained another injury, leaving his participation over the remaining few weeks of the season - assuming Barca reach the Champions League final - in doubt.
Philippe Coutinho, who spent five years with Liverpool prior to joining the Spanish side in January 2018, is now almost certain to get the nod alongside Suarez and Messi, as was the case in the first leg.
In fact, with Rafinha the only other injury concern, Valverde could well use the same XI that started last Wednesday. Arturo Vidal was preferred to Arthur and Sergi Roberto got the nod over Nelson Semedo - two places that remain up for grabs.
Messi has 12 Champions League goals for Barcelona this season - just two shy of his best ever tally in a single season when scoring 14 in 2011-12. The Argentinian has netted more goals against English teams than any other player in the competition's history (26), including six this season.
Liverpool possible starting lineup:
Alisson; Alexander-Arnold, Matip, Van Dijk, Robertson; Henderson, Fabinho, Wijnaldum; Shaqiri, Origi, Mane
Barcelona possible starting lineup:
Ter Stegen; Roberto, Pique, Lenglet, Alba; Rakitic, Busquets, Vidal; Messi, Suarez, Coutinho
Head To Head
Barcelona have won both of their previous Champions League visits to Anfield against Liverpool, coming out on top 3-1 in November 2001 and 1-0 in March 2007, though they crashed out on away goals in that last-16 tie 12 years ago.
That makes the Catalan giants the only away side to win more than once at Anfield in the Champions League era.
This is the 10th meeting between the sides overall, six of which came in a six-year period between 2001 and 2007. Each side has now recorded three wins, with Barcelona scoring nine goals to Liverpool's six, though the Premier League side have won all three two-legged contests on aggregate.
We say: Liverpool 1-1 Barcelona (1-4 on aggregate)
Liverpool are aiming to become only the third team in the history of the European Cup to come from three goals down after the first leg of a semi-final and progress to the final - Panathinaikos in 1971 and Barcelona in 1986 being the others.
The Reds know all about what it takes to pull off a famous European comeback, and their opponents have more recently been on the wrong end of a three-goal turnaround, but Barca will be at pretty much full strength and should be able to see the job through to remain on course for a famous treble.