It was Haaland who opened the scoring at Selhurst Park when he headed home the 1-0 goal in the 17th minute.
Early in the second half, Rayan Cherki doubled City's lead, before the home side reduced the deficit when a free kick went past goalkeeper Gianluigi Donnarumma. But Cherki soon scored his second goal in five minutes to make it 3-1.
In the closing stages of the match, Haaland scored his second goal after a pass from Phil Foden.
Haaland wore a mourning band to honour Norway's King Harald V, who died on Friday morning. Crystal Palace striker Jørgen Strand Larsen also wore a mourning band.
All Norwegian players in the Premier League will wear mourning bands during this weekend's matches after an appeal to the league, according to Norwegian Viaplay.
