Cody Gakpo scored his fifth goal for Liverpool since joining the club in January
The Reds had not won since putting seven unanswered goals past Manchester United at the start of March but after a slow start they ruthlessly dismantled Javi Gracia's hapless side.
Trent Alexander-Arnold used an arm to control the ball but neither the referee or the VAR felt it worthy of penalising and he drove forward to exchange passes with Salah and set up Cody Gakpo for the opener.
The Egypt forward doubled his side's lead soon after, firing a sweet shot in after being set up by Jota to put the visitors in control.
Leeds were given hope after the break when Luis Sinisterra dispossessed the ponderous Ibrahima Konate and cleverly chipped the ball beyond Alisson.
However, Liverpool quickly responded through Jota's neat finish as the Portugal forward notched his first goal since April 2022.
After seeing a goal ruled out for offside, Salah then slotted home his second at the end of a superb move to put the game to bed before Jota grabbed his second when he steered in a Jordan Henderson cross.
Substitute Darwin Nunez completed the rout with a neat side-foot finish against a shambolic Whites side, who conceded five last weekend at home to Crystal Palace and now have the worst defensive record in the Premier League.
On an encouraging night for the visitors, there was also a return to action for Luis Diaz as the Colombia winger made his first appearance since October as a late substitute.
Jurgen Klopp's side remain eighth in the Premier League table, a point behind seventh-placed Brighton and two shy of Aston Villa in sixth.
Both teams will be happy to see the back of the 2022-23 season, but while Leeds' campaign may still tip into the misery of relegation, Liverpool could yet salvage something from the wreckage.
There have been some highlights from their campaign - notably the seven goals scored against Manchester United - but this season has been largely a struggle, with injuries and lack of form affecting key players and new recruits taking time to familiarise themselves with their new club.
Life has been especially tough on the road, with Monday's win just their fourth away from Anfield all season.
They remain well short of the remarkable consistency they produced for numerous seasons under Klopp, but they demonstrably retain the ability to be ruthless when given a sniff of opposition weakness.
Gakpo's opener was perhaps controversial but it was also clinical, as Alexander-Arnold exploited the space left by the dispossessed Firpo and centred for Gakpo to tap home.
They were equally quick to take advantage four minutes later, when the ball was won by Jota and Salah was teed up to fire in a superb finish.
The third, fourth and fifth goals were no less clinical thanks to some slick passing and brilliant finishing from Jota and Salah, who now has nine goals against the Whites in his Liverpool career.
The Reds, who were much more like the hard-running side witnessed in recent seasons, had only seven shots on target in the game.
Klopp's side is facing its first finish outside the top four in seven seasons, and with Aston Villa and Brighton in superb form above them, the very real prospect of no European football at all for the first time since 2016-17.
There is work to be done and summer signings will inevitably be made, but reports of their demise are perhaps a little exaggerated.
Leeds began this campaign with assurances from their owner Andrea Radrizzani that having come perilously close to relegation last May, a repeat 12 months later was "impossible".
With May rapidly approaching again, here the Whites are once more, two points above the bottom three with back-to-back home embarrassments and seven stressful games to go.
Having suffered a demoralising second-half demolition at the hands of Palace in their previous game, this result could be terminal to their confidence.
For 35 minutes, their tactic to contain and counter-attack worked reasonably well but, having suffered a setback with the opener, they were unable to regather themselves.
There was a bit of fight in the second half thanks to Sinisterra's dogged determination and cute finish but as against Palace, once the floodgates opened, they were unable to shut them again.
With all four of the sides below them in the table losing at the weekend, Leeds have not slipped any further into trouble. But their goal difference has now taken a battering thanks to the first occasion they have conceded five or more goals in successive games in their history.
A rally is needed, with upcoming fixtures against Fulham, Leicester and Bournemouth potentially the key to their fate.
--- Courtesy of BBC Sport