The exciting win was a fifth in a row for Mercedes in Monza, the spiritual home of the most glamorous and successful team of the sport, and one of the most satisfying of Hamilton.
"Today was so difficult, even though the negativity is never great, I've got something done about it, I actually accept it," Hamilton said as the crowd plodded him on the stage.
"I love being here in Italy … the track is incredible, and it's an honor to win here for such a big crowd."
Hamilton's sixth win of the season takes him to 256 points, to 226 of his German rival, with seven races left in what remains a fierce battle between the four-time world champions.
Mercedes has 415 points for Ferrari's 390 in the constructors' classification.
Raikkonen had a chance to win his first victory in 108 races, but the Finn, who took the lead after Hamilton had beaten him in the fourth round, was unable to keep the Brit off.
Hamilton passed him eight laps from the end and never looked back.
"I think it (the car) was fast enough, but unfortunately our rear tires went", said Raikkonen, who was hardly in the mood to celebrate his 100th podium in Formula 1.
"It was a losing battle from that point on, we did our very best," said the world champion of 2007. "We certainly tried, but the rear tires gave up before the race ended."
The winner was also significantly helped by teammate Valtteri Bottas, who after Hamilton went on the job and managed to hold Raikkonen long enough for the other Mercedes to catch up.
"I really tried to do everything I could to go to the podium." At first my mission was to keep Kimi off, and then I challenged Max, "Bottas said.
Vettel, who made two stops, including a first to replace a damaged front wing, and Bottas both to a spot at the finish after Red Bull's Max Verstappen got a five-second penalty to clear the Fin of round 44 to push. Verstappen's Red Bull team-mate, the Australian Daniel Ricciardo, could not finish.
Verstappen finished fifth with Romain Grosjean sixth for Haas and Esteban Ocon seventh for Force India ahead of teammate Sergio Perez.
Renaults Carlos Sainz was ninth and Canadian Lance Stroll took a point for Williams' wrestling in 10th place.