Salah was brought down by Mamadou Sakho inside the area minutes before the half-time break.
James Milner, who has scored 13 out of 15 penalties in the Premier League, stepped up to convert as he sent Hennessey the wrong way.
The Reds lead 1-0 at the break, having matched Crystal Palace's hunger for the game. Palace have hit the crossbar with a rousing shot from Andros Townsend, but the Reds have controlled their attack well otherwise.
More to follow.
Watch the penalty call and goal below.
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