Salah also forced another brilliant save from Wayne Hennessy from close range.
He penalised Mane for deliberate handball but, somehow, didn't deem it worthy of a second yellow card.
Luka Milivojevic scored Crystal Palace's first goal in the 13th minute of the game.
The winger showed great composure to tuck home Andrew Robertson's cross from the left, his 37th goal in all competitions securing a morale-boosting result ahead of the mouth-watering Champions League quarter-final against Manchester City in midweek.
"We didn't play the best football we can play, no problem with that but it helps, especially in the Premier League".
The Egyptian duly dominates our Seven Deadly Stats from the game.
More snow: Forecast calls for 3 to 5 inches Friday, Saturday
Avery said it will be breezy with northwest winds between 10 and 15 miles per hour , however, making it feel a little cooler. Vining said the snow will likely contain between a quarter and a third of an inch of moisture, making it wet and heavy.
Salah proved to be the match-winner once again, however, as the Egypt global fired a low Andrew Robertson cross past Hennessey in the 84th minute to break Palace hearts late on.
Roy Hodgson's side squeezed the space expertly, were happy to cede possession for long periods and knew that when the ball was won, they had a weapon capable of making a difference at the other end.
The former Liverpool striker sent an attempted lob well wide with just Karius to beat and then shot over the bar after Van Dijk had been caught in possession by Andros Townsend.
Even after Liverpool had responded and equalised, Palace grew in confidence and started to create more in attack.
Christian Benteke, failed to capitalize on two golden chances.
Grant Hill to enter Basketball Hall of Fame
Ray Allen, who holds the record for most 3-pointers in National Basketball Association history, was also on that list. Two ex-Mavericks are among the Naismith Basketball Hall of Fame's Class of 2018 , reports said Thursday.
Liverpool, meanwhile, have moved above Manchester United into second position.
Liverpool's victory was only tainted by Adam Lallana's injury.
Adam Lallana's miserable luck continued as he lasted only a few minutes before suffering yet another muscle injury.
If more tangible progress is to be made, Klopp will have to develop his artillery beyond the current Big Three.
"It was no dive; diving with a bit of contact is not possible", said Klopp.
"The dirty three points are very often the most important, and they were really dirty today!"
Sisi heads for landslide win with low turnout
Egypt's election commission said the vote would be free and fair, and Sisi said he wished more candidates had run. The President won with about 92 per cent of the vote, according to preliminary results on Thursday.