The 26-year-old German, series leader and defending triple world champion, survived a torrid start and gearbox problems to dominate an intriguing 53-lap race.
Vettel came home 5.4 seconds clear of Ferrari's Fernando Alonso, ahead of third-placed Australian Mark Webber in the second Red Bull and Brazilian Felipe Massa, fourth in the second Ferrari.
Vettel reeled off his sixth win of the season - the 32nd of his career, equalling Alonso's total. It was Vettel's third win at Monza - and greeted by loud booing during a dramatic podium ceremony.
"It was a fantastic race, but you can hear the difference when you don't win here in a red suit," said Vettel.
"But this means you have done well and beaten the red men! It was a great team effort today. The race was terrific for both of us as we had problems with the gearboxes at the end, but I was ok because I had a good cushion. It is a fantastic win."
Briton Lewis Hamilton, who started 12th, lost the use of his team radio and suffered a slow puncture, but he fought back twice to finish ninth.
"It is a nightmare weekend for me. It's a real shame, but these kinds of things happen. It has been a good year - we're just going to keep pushing," he said before conceding it had become virtually impossible for him to win the title.
"Fantastic Seb! You've won the Italian Grand Prix again," said Red Bull chief Christian Horner. "A brilliant drive..."
German Nico Hulkenberg came fifth to endorse his claims as a possible successor to Massa next season.
"I can't say I am not interested in this - it's a no brainer and we just have to wait and see."
Compatriot Nico Rosberg finished sixth in the leading Mercedes ahead of Red Bull-bound Australian Daniel Ricciardo of Toro Rosso and Frenchman Romain Grosjean of Lotus.
Hamilton finished ahead of Briton Jenson Button of McLaren, celebrating their 50th anniversary in Formula One.
With seven races outside Europe remaining, Vettel leads with 222 points from Alonso (169) and Hamilton (141).
Horner added: "The races we are meant to be weak at, we keep winning. It has been a fantastic weekend - to win at an historic track like Monza is amazing."
Alonso said: "Second place is good and to have this podium ceremony which is the most spectacular podium of the year."
Webber, who collected his first trophy from an Italian race, said: "It was a good battle with Alonso, but a great team result."