Luka Milivojevic had given the Eagles the lead with an early penalty, but a second half goal from Sadio Mane and Salah's strike with just six minutes remaining means Palace have now lost six of the last seven Premier League games.
Four minutes after the break Sadio Mane brought Liverpool level, finishing James Milner's left-wing cross.
For the second time running Benteke should have restored the lead as Palace capitalized on a mistake from Virgil Van Dijk, the Belgian attempted a chip but was too high from goal.
Mane was then fortunate to escape a second yellow when he deliberately handed the ball just outside the Palace box, and from the resulting free kick, Karius made a flying save to deny Patrick Van Aanholt.
Lallana was carried off on a stretcher at Selhurst Park and Klopp later said his player had a suspected muscular injury.
Liverpool continued to apply pressure; Salah looped a volley wide, but when Palace did attack, they never looked secure.
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Wilfried Zaha terrorised Liverpool's defence and Trent Alexander-Arnold in particular.
They then defended well - keeping Salah out of action and frustrating Mane.
Salah's also about to steal a record that has been the domain of Manchester United players so far, something that will no doubt make Liverpool fans happy.
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.
FW Mohamed Salah, 6 - Palace did a fine job keeping him quiet for most of the game but it only takes one lapse for the Egyptian to pounce.
Wayne Hennessey - 6 - Did his job for most of the game and wasn't at fault for the goals.
Klopp quickly replaced the Senegalese and Liverpool took advantage when despite having one of the quieter games of an incredible debut season at the club, Salah proved the match victor.