The Briton and Sebastian Vettel, his closest title rival now 30 points behind, collided on the opening lap with the German Ferrari driver sent spinning down to 18th place before recovering to fourth.
Hamilton then twice overtook Kimi Raikkonen, who had started on pole, to dampen the spirits of Ferrari fans who had turned out in droves in the hope of celebrating a first home win in eight years.
The thrilling victory was a fifth in a row for Mercedes at Monza, spiritual home of the sport's most glamorous and successful team, and one of Hamilton's most satisfying.
Hamilton's sixth win of the season lifted him to 256 points, to his German rival's 226, with seven races left in what remains a fierce battle between the four-time world champions.
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Mercedes have 415 points to Ferrari's 390 in the constructors' standings.
Raikkonen had looked to be in with a chance of his first win in 108 races but the Finn, who seized back the lead after Hamilton passed him on lap four, was unable to hold off the Briton.
Hamilton passed him again eight laps from the end and never looked back.
The winner was also helped considerably by team mate Valtteri Bottas who led after Hamilton pitted and managed to hold up Raikkonen long enough for the other Mercedes to close the gap.
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Vettel, who made two stops including a first one to replace a damaged front wing, and Bottas both moved up a place at the finish after Red Bull's Max Verstappen was handed a five second penalty for pushing the Finn off track on lap 44.
Verstappen was fifth with Romain Grosjean sixth for Haas and Esteban Ocon seventh for Force India ahead of team mate Sergio Perez.
Renault's Carlos Sainz was ninth and Canadian Lance Stroll took a point for struggling Williams in 10th.
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