By Emma Sanders
BBC Sport
Salah has now scored 29 goals in the Premier League this season
Mohamed Salah's late goal snatched a victory for Liverpool at Crystal Palace and left their hosts two points above the relegation zone.
The Egyptian took a touch before firing past keeper Wayne Hennessey after Andy Robertson had crossed in from the left.
Luka Milivojevic had converted from the spot early in the first half to give Palace the lead after Liverpool keeper Loris Karius took out Wilfried Zaha.
And Sadio Mane turned in James Milner's cross shortly after the break to level.
Liverpool had plenty of chances to score in the first half at Selhurst Park as Salah's curling effort tested Hennessey and Mane came close with two headed efforts.
Karius' early error looked costly as Palace clung on until half-time but Liverpool responded within four minutes of the restart when Milner and Robertson combined down the left to set up Mane.
Christian Benteke then missed two clear goalscoring chances in as many minutes before Patrick van Aanholt's fizzing free-kick was palmed away by Karius.
There were appeals for Mane to be shown a second yellow card - he was booked for diving in the first half - after he picked up the ball on the edge of the area but referee Neil Swarbrick settled for a free-kick.
The Reds then completed the comeback when Salah scored his 29th Premier League goal of the season - equalling the league record of scoring in 21 matches in a 38-game season.
Salah saves Liverpool's blushes
Liverpool headed to Selhurst Park knowing they have an important week ahead.
The Reds host Manchester City in the first leg of their Champions League quarter-final on Wednesday before making the short trip to Merseyside rivals Everton in next Saturday's Premier League derby.
But Jurgen Klopp named a strong starting line-up in his 100th Premier League game in charge despite expectations he would rest several key players.
But Liverpool's first-half performance did not match the boldness of Klopp's selection as they lacked intensity and imagination against a stubborn Palace defence.
Mane's equaliser early in the second half was a good response but Benteke missed two great chances moments later to regain Palace's lead.
Liverpool had further chances and so did Palace but it was Salah who once again came to the rescue - saving the visitors' blushes.
Victory takes Liverpool up to second place in the Premier League table - at least for a few hours as Manchester United host Swansea at 15:00 BST.
More missed opportunities for Palace
Benteke should have given Palace the lead in the second half but he missed two great chances
Roy Hodgson's side suffered yet another defeat against a team in the top six and, having taken an early lead, this was a missed opportunity.
Palace were the better side in the first half and deserved to be in front after Zaha had won a penalty when he was clattered by Karius.
They then defended well - keeping Salah out of action and frustrating Mane.
Even after Liverpool had responded and equalised, Palace grew in confidence and started to create more in attack.
But Benteke missed two golden opportunities to regain the lead and it ultimately proved costly as Salah showed the required prolificacy at the other end.
Palace have now suffered five defeats in their last six games and are two points above the relegation zone - with their rivals all still yet to play.
After throwing away leads against both Manchester United and Liverpool in the space of a month, Salah's late winner will come as yet another blow to the south London side.
Man of the match - Andy Robertson
Andy Robertson was involved in the build-up to both Liverpool goals in the second half
What's next?
Crystal Palace travel to Bournemouth in the Premier League next Saturday (15:00 BST).
Liverpool host Manchester City in the quarter-finals of the Champions League on Wednesday (19:45 BST) before travelling to Goodison Park for the league's Merseyside derby on Saturday (12:30 BST).