The Merseyside club looked set to record a comfortable home victory when Adam Lallana found the back of the net 26 minutes into the game.
The games turning point came just before half time when Jason Puncheon scored a close range free-kick.
Can received a rating of 7.53 , the highest of any Liverpool player on the day. The 21-year-old made eight tackles, one interception and four clearances.
The Germany U21 international also made a total of 67 passes and maintained a passing accuracy of 83.6%.
Kick-off: 17:30 (GMT)
Referee: J Moss
Liverpool: Mignolet, Can, Skrtel, Lovren, Moreno, Gerrard, Henderson, Lallana, Coutinho, Ibe, Sterling
Subs: Ward, Johnson, Toure, Lambert, Lucas, Allen, Sinclair
Crystal Palace: Hennessey; Ward, Dann (C), Kelly, Souare; McArthur, Ledley, Puncheon; Lee, Bolasie; Chamakh.
Subs: Speroni, Delaney, Jedinak, Mutch, Zaha, Campbell, Murray
Goals: .26 Lallana, .43 Puncheon, .60 Zaha, .90+1 Murray