The score was 1-0 at the time, Milner having slotted in the penalty on the stroke of halftime after Salah tumbled under a challenge from former Liverpool defender Mamadou Sakho.
Luka Milivojevic's free-kick forced a flying save from Alisson early in the second half, but hopes of a home fightback were extinguished with 15 minutes to go when Wan-Bissaka walked for bumping over Salah as the Egypt global raced through on goal.
Liverpool dominated possession early on but Palace nearly took the lead when Andros Townsend hit the crossbar midway through the first half with a stunning long-range strike.
Crystal Palace v Liverpool - Selhurst Park, London, Britain - August 20, 2018 John Aldridge has been impressed with new Liverpool signing Naby Keita. "Together with Virgil, they have a very good understanding - on a personal level as well and that's really cool". "Today we weren't brilliant but we won".
An angry Hodgson disagreed with Michael Oliver's decision to award Salah a penalty and said Palace should have had a spot-kick of their own when Max Meyer went down in the box. He's trying to defend.
Roberto Firmino's pass found Salah just inside the Palace area and when Sakho caught him with an out-stretched leg, the Egyptian's slightly delayed tumble didn't dissuade Oliver from giving the penalty. There is no way he is looking to get contact on the player at all. I don't think the big teams ever win here comfortably. "I'm more interested in the fact we played really well".
After rattling the crossbar with a long-range shot in the first half, Andros Townsend struggled to find an end product in the second half with Andrew Robertson enjoying another excellent match.
Southampton manager Mark Hughes called into question Jon Moss' fitness last season when he accused the referee of failing to keep up with play.
"He loves playing with these boys, and that's the most important thing".