Liverpool had taken the lead just before the break when James Milner converted a penalty, before Palace had things go from bad to worse when Aaron Wan-Bissaka was sent off for a foul on Mohamed Salah.
As the game entered the final minutes, Crystal Palace felt thaty had to go for an equalising goal and were attacking in numbers on the opposition goal.
After they were awarded a corner, the resulting ball was dealt with and was played out to Mohamed Salah.
The Egyptian went forward and played a through ball to Sadio Mane, who used his pace to get in on goal.
Patrick van Aanholt did his best to get back, but Mane was too quick and was able to go round the keeper and pass the ball in to the net, to get his third goal of the season.