Adam Lallana opened the scoring for Liverpool on 26 minutes after a horrible error for Crystal Palace defender Martin Kelly.
The Reds old boy misplaced a pass to his defensive partner Scott Dann, who was immediately chased down by Lallana.
The Liverpool fan, Dann, attempted to stop the ex-Southampton midfielder with a diving tackle, but Lallana rode the challenge before finding himself one-on-one with Wayne Hennessey.
The Welsh goalkeeper was given no chance as Lallana sent a deliberate finish into the top corner.
The fixture—both sides’ penultimate match of the Premier League season—began with a celebration for Liverpool captain Steven Gerrard.
The Anfield legend and one-man club was honoured before the match and given a guard of honour as he entered the stadium for his final match in front of his beloved Kop.
Liverpool head into the fixture in fifth in the Premier League, looking to confirm their place in the Europa League for next season.
Palace, meanwhile, find themselves in 12th.