Haaland, who averaged almost a goal per game in the Bundesliga for Borussia Dortmund before his move to City in June, has now scored six times in his opening four league matches for Pep Guardiola's side.
The win moves City to the top of the table, level on 10 points with Brighton & Hove Albion. Palace are 13th with four points from their opening four games.
Haaland was given a standing ovation when he was substituted six minutes from the end but at halftime City were staring at a possible repeat of their 2-0 home loss to Palace last season.
An own goal from John Stones in the fourth minute put Patrick Vieira's side ahead and then the visitors doubled their lead when an unmarked Joachim Andersen powered in a header from an Eberechi Eze corner in the 21st minute.
City struggled to find their fluency but the almost inevitable comeback started in the 53rd when Bernardo Silva cut in from the right and his low shot took a slight deflection and beat goalkeeper Vicente Guaita.
Guardiola then made a double substitution and moved Phil Foden to left back and within a minute he had delivered a pinpoint cross which Haaland met with a fine glancing header.
The striker then turned the ball in from close range after a clever move inspired by Silva and saved the best for last -- showing Ilkay Gundogan the pass he wanted to run onto and then holding off Joel Ward as he fired into the bottom corner.
"It was a proud moment for me and my family and I'm so happy. Amazing feeling to score a hat-trick," Haaland said.
"It's about trying to continue what we are doing. It was about small adjustments and we did that and got results. We had to listen to the manager".
Haaland said it was important that City did not panic after Palace's early goals.
"It's a mentality that we trust each other and we know the chances will come. It's about keeping going. In the end we scored four goals and that's a really good thing.
"It's a warning that we have to become better, training hard and develop. When we play at home we shouldn't concede early goals. It's about working harder," he said.