Hamilton finished nearly five seconds ahead of Mercedes team-mate Valtteri Bottas, while Vettel came third in his Ferrari, more than half a minute behind.
Hamilton now has 238 points, three more than Vettel with seven races remaining. Next stop is Singapore in a couple of weeks.
“It’s obviously an incredibly exciting season and the last two races have been incredibly strong for us as a team,” Hamilton said.
Vettel had led the standings all season but Ferrari struggled in rainy qualifying conditions on Saturday and couldn’t match Mercedes’ race pace either, on a Monza circuit featuring long straights and high speeds better suited to Mercedes’ outright power.
“Mercedes power is definitely better than Ferrari power,” Hamilton said. “So it worked well this weekend.”
After getting out of his car, Hamilton first greeted Bottas then jumped into a crowd of Mercedes team members. The British driver was met with a mix of cheers and boos during Monza’s famed celebration with the podium suspended over the track.
“You know what? I love it here in Italy and I love the passion of the Ferrari fans,” Hamilton told a sea of red-clad Ferrari fans who invaded the track. “We don’t get to see this energy anywhere else, apart from maybe Silverstone.
“To get one-two here is incredible. I know it’s not easy for Ferrari fans to accept.”
The Ferrari supporters were hoping for more on a weekend celebrating the car manufacturer’s 70th anniversary.
“This race was difficult, I know. But we’re coming,” said Vettel, who has now won just one of the last seven races. “We didn’t have the pace of Mercedes today.”
It was Hamilton’s 59th career win and second consecutive triumph after posting a harder-fought victory in Belgium the previous weekend.
Red Bull’s Daniel Ricciardo finished fourth, having climbed through the field from a 16th-place start due to a grid penalty.
Kimi Raikkonen crossed fifth – exactly where he started – in the other Ferrari.
Force India’s Esteban Ocon placed sixth and 18-year-old Lance Stroll settled for seventh after becoming the youngest F1 driver to start on the front row in his Williams.
As drivers gathered at the front of the grid for the national anthem ahead of the race, air force jets flew low overhead emitting a trail of smoke in the green, white and red colours of the Italian flag.
Hamilton got off to a clean start and Bottas moved up from fourth to put Mercedes one-two after only four laps.
Raikkonen battled with Bottas early on but then went off course and had to slalom through the barriers.
“I have damage on the rear of the car,” Raikkonen said via team radio. But Ferrari told the Finn they couldn’t see anything. “I don’t know to fix it,” Raikkonen replied.
Meanwhile, Vettel slipstreamed past Ocon down the main straight to move into third but he, too, then reported problems with the rear of his car and kept dropping further behind the Mercedes cars.
“It took a while before I could really trust the car,” Vettel said. “And then we were isolated.”
Hamilton’s only hiccup came when he skidded on to the edge of the gravel briefly midway through the race. Otherwise, he and Bottas were gaining half a second per lap on the Ferraris and the Briton’s victory was a comfortable one.