Chris Wilder's side, who have already taken points from trips to Chelsea, West Ham, Tottenham and Arsenal this season, were indebted to a mistake from home goalkeeper Vicente Guaita for the only goal of the game.
Hodgson's men created their first clear-cut opportunity of the match with 25 minutes gone when Jordan Ayew embarked on a mazy run and played Benteke through – but the Belgian could only hit the side-netting from an angle.
The Eagles looked the most likely to open the scoring and they wanted Baldock sent off with 10 minutes of the first half left following another foul on Zaha – but Madley afforded the full-back another life.
The Ivorian was causing United all sorts of problems and saw a cross agonisingly drift across the face of goal without a decisive touch, then minutes later Van Aanholt fired over.
Barely three minutes of the second half had been played before a lengthy stoppage occurred when Benteke and Chris Basham needed treatment after clashing heads.
After they were fine to continue, both sides looked for the opener and it finally arrived in the 58th minute – and in bizarre fashion.
Norwood curled a corner to the front post and Guaita grabbed the ball unchallenged, but dropped it over the goal line to gift the visitors the lead.
The Blades midfielder almost had a second three minutes later, but his free kick was saved well by Palace's goalkeeper.
Chances were coming more frequently now and James Tomkins should have levelled with 20 minutes left, but the Palace defender headed McArthur's cross wide.
VAR and in particular the pitchside monitor took centre stage with 72 minutes on the clock when Ward was dismissed for a tackle on Enda Stevens.
But referee Madley was told to check the decision using the screen by the side of the pitch and after doing so rescinded his red card to a yellow.
Stevens had two late chances to wrap up the game for Wilder's side and despite failing to take them, they held on to complete a double over the south Londoners.