Salah also forced another brilliant save from Wayne Hennessy from close range.
Mamadou Sakho joined Benteke up front as the clock ticked into four minutes of added-time, but Palace failed to break down a compact Liverpool defence.
Christian Benteke missed the first of two fine chances against his former team when a header from Milivojevic sent him one-on-one with Karius before his composure deserted him and he hooked harmlessly wide.
He penalised Mane for deliberate handball but, somehow, didn't deem it worthy of a second yellow card.
Salah is now just three goals short, of becoming the first Liverpool player ever to score 40 goals in a single season, since Ian Rush achieved the feat back in the 1986-87 season.This intensifies the race for the Golden boot this year.
Maybe Lallana only picked up a slight knock and will be back in time for Liverpool's Champions League clash against Man City on Wednesday.
Sadio Mané became the joint-highest scoring Senegalese player in Premier League history, equalling Demba Ba's haul of 43 in the competition. Liverpool needed this win, but they left south London with as many questions as answers.
Roy Hodgson faces some difficult selection decisions ahead of Palace's game on Saturday
It was then that Mane attempted to impose himself.
Even after Liverpool had responded and equalised, Palace grew in confidence and started to create more in attack.
Liverpool, meanwhile, have moved above Manchester United into second position.
Lallana's injury takes some of the gloss off the victory for Liverpool.
England star Adam Lallana's rotten injury luck strikes again, the midfielder carried off on a stretcher just five minutes into a second-half cameo - to raise fresh doubts about his ability to be fit for the summer's World Cup in Russian Federation.
But it was not what he or Klopp had hoped for when he hobbled off within three minutes of his introduction.