Salah struck the opener, finding the net for his seventh appearance in a row for the Reds, maintaining a stunning run of goalscoring since arriving at Anfield from Roma.
Newcastle deployed a packed defence but Salah found a way through before half-time, finishing off Alex Oxlade-Chamberlain's pass to put Liverpool on track for a solid win ahead of Tuesday's Champions League visit of Porto.
And when Liverpool cut Newcastle open again, Sadio Mane finishing off a fine team move to score the 200th league goal of Jurgen Klopp's reign, the game was effectively over as a contest.
Benitez's men rarely looked like scoring, with Newcastle left 16th in the table and just two points above the relegation zone, with captain Jamaal Lascelles seemingly fortunate not to see red in stoppage time for a push on the clean-through Salah.
Liverpool climb above Manchester United into second and Klopp's men have built a seven-point cushion from fifth-placed Chelsea in the race to secure Champions League qualification, with Antonio Conte's side in action at the Premier League's runaway leaders Manchester City on Sunday.
200 - Sadio Mané's goal was the 200th that Liverpool have scored in the Premier League under Jürgen Klopp. Since he was appointed, only Man City (214) have scored more often in the competition. Exciting. pic.twitter.com/uBFXMpplaO — OptaJoe (@OptaJoe) March 3, 2018
Mane's heavy touch denied the winger a sight of goal in the early minutes, while Salah sent a volley into the side-netting, but both attackers would find the target later.
Florian Lejeune's ambitious long-range free-kick posed no problems for Loris Karius, Martin Dubravka showing sharp reflexes to keep out a Dejan Lovren header at the other end.
Newcastle's determined defending was denying Liverpool space, but Salah dallied when he could have fired at goal, Lejeune recovering to make a block.
Salah did not waste his next opportunity, though, breaking the deadlock in the 40th minute to score his 32nd goal of the season in all competitions.
A ricochet in midfield fell to Oxlade-Chamberlain, who fed Salah for the Egypt international to take a sharp touch out of his feet and hit a crisp finish through the legs of Dubravka.
Karius made a brilliant save high to his right to palm over a looping Mohamed Diame strike after Mikel Merino's backheel teed up a first-time drive.
Salah wanted a penalty for handball early in the second half when Lascelles blocked his shot in the box, but referee Graham Scott waved his appeals away.
Liverpool doubled their lead in the 55th minute, though, with Mane on target for the third game in a row in all competitions.
Beautiful passing combinations and superb movement led to Roberto Firmino setting up Mane, with the Senegal forward - involved earlier in the sweeping attack - beating Dubravka with a super curling strike.
The intensity dropped from Klopp's men thereafter, their energy levels protected ahead of Tuesday, but there was never any sign of a Magpies fightback and Lascelles somehow avoided punishment when he brought down Salah on the edge of the box with the last action of the game.
Newcastle have not won at Anfield since 1994 and they were largely toothless here, Benitez's side slipping closer to the relegation zone after a tame defeat, but Liverpool continue to thrive following the sale of Philippe Coutinho to Barcelona.
Key Opta Stats:
- Liverpool are now unbeaten in 22 successive home league games against Newcastle United (W18 D4 L0).
- The Reds have scored more Premier League goals against Newcastle than they have versus any other side in the competition.
- Salah has scored in each of his last seven games for Liverpool in all competitions – the last player to do so in more successive matches was Daniel Sturridge in February 2014 (8).