Jurgen Klopp's side were unable to work their attacking magic for the majority of play with former Liverpool boss Rafa Benitez sending his Newcastle side out to stop the Reds running riot as they have done on many occasions already this season.
The visitors, opting for two defensive midfielders in the centre of the park, stifled the Reds for the majority of the first-half but as ever, Klopp’s side found a way to put the ball in the back of the net.
Salah, with his 32nd goal of the season, opened the scoring before the 40-minute mark following up on a sweeping counter-attack. Alex Oxlade-Chamberlain won the ball inside the centre-circle and raced forward through the heart of the Newcastle defence.
The England international then slid a pass to the unmarked Salah inside the 18-yard-box. His shot clipped the foot of Martin Dubravka but squirmed its way under the goalkeeper to give the hosts a 1-0 lead.
Mane doubled the lead ten minutes into the second-half.
The forward timed his run to perfection as Roberto Firmino rolled the ball between the Newcastle centre-halves. Mane, one on one with Dubravka, swept the ball home to the right of the goalkeeper, doubling the Reds lead.
Reds frustrated but find a way
Liverpool had lots of early possession but were unable to carve Newcastle open as they would have liked in a largely uneventful first-half. One chance fell to Mane but he slipped before he could take a second touch and open himself up to shoot.
The visitors, who clearly set out looking to play on the break and to find Dwight Gayle through the channels with plenty of direct and lofted balls, sat back and waited. Gayle was able to wriggle free of Dejan Lovren on a handful of occasions but didn’t trouble Lorius Karius.
There were a few chances for the hosts but for 39 of the first 40 minutes, they were unable to find their scoring touch.
Klopp’s side won the ball high up the pitch with Emre Can. He squared to Mane who finds an unmarked Salah on the right-hand side of the area. Salah wriggled away from one defender but his eventual shot was blocked for a corner.
From the resulting corner, Lovren heads at goal but Dubravka can only push the effort away. Lovren tried to follow up with another header but the ball looped skywards and fell to Mane but before he could shoot, the Magpies clear.
Karius keeps the Reds ahead
Despite not threatening all too much in the first 45, Benitez's side had one effort that could have levelled proceedings.
Karius saved spectacularly from Mo Diame after Newcastle worked a chance in the Liverpool box. The ball rolled out to Diame on the edge of the box and his effort - arrowing certainly for the top right-hand corner - was pushed away by the German keeper.
The Kop rose to acknowledge the brilliance of the stop before referee Graham Scott paused proceedings for half-time.
Reds wrap up the win
Unlike the first-half, it didn’t take long for the Reds to find the back of the net in the second-half.
Mane, darting between the lines, found a way past a beaten Dubravka to double the host lead.
Yet, similarly to the first 45 minutes, the hosts were unable to work their forward magic - instead, beating the Magpies on the break.
After the goal, proceedings slowed down with the hosts looking to see out the result.
The visitors had a penalty shout waved away by referee Scott but failed to test Karius on the same level as Diame's effort at the end of the first-half.
Klopp's side had their own penalty shout right at the end of stoppage time but were denied by referee Scott as he looked for assistance from his linesman.
With the win, Liverpool now move up to second in the Premier League table but sit 15 points behind leaders Manchester City.
Klopp's side will now prepare for Tuesday's Champions League meeting with FC Porto as they look to secure passage into the next round.
The Reds picked up a 5-0 win in Portugal and will be hoping not to be on the end of a record aggregate score overturn in the Champions League.
Newcastle remain 16th, two points above the drop zone. Next time out, they face Southampton at St James' Park in a crucial fight at the wrong end of the table.