Hamilton, who broke Michael Schumacher's record for the most pole positions on Saturday, made no mistake at the beginning of the race and, with some help from Mercedes' teammate Valtteri Bottas - who finished 2nd - never looked troubled as he secured his third win in the last four races.
The result moves him three points ahead of German driver Vettel, who held off the challenge of Red Bull's Daniel Ricciardo. The Australian was the star of the day, moving from 16th to 4th with a display of bold, aggressive driving, while his teammate Max Verstappen overcame an early puncture that saw him in last position to finish in the points in 10th.
Vettel had led the standings all season but Ferrari struggled in rainy qualifying conditions Saturday and couldn't match Mercedes' race pace, either, on a Monza circuit featuring long straights and high speeds better suited to Mercedes' power.
"We didn't have the pace of Mercedes today but we have a very strong car and will finish the season very strongly," said Vettel.
It was Mercedes' third one-two this season and the team's 39th overall.
“I love it here in Italy and I love the fans," Hamilton said after the race. "This energy is like nowhere else apart from Silverstone.”
Seven races, all outside Europe, remain in the 2017 F1 season, with the next in Singapore on September 17.
As it happened
HAMILTON WINS THE ITALIAN GRAND PRIX!
That’s Hamilton’s third win in the last four Grand Prixs and takes him above Vettel (3rd) in the driver’s standings for the first time in 2017. He was never really troubled here, leading from the front with Valeri Bottas (2nd) blocking any progress from behind. There were great recovery drives from Red Bull’s Max Verstappen and Daniel Ricciardo. Full report to follow shortly.
As Hamilton serenly progresses to the win, it seems Verstappen was investigated for "forcing another driver off track" after an incident with Magnussen but has laready been cleared of any wrongdoing.
Hamilton is going to win but it's been all about the Red Bulls today. Ricciardo has driven sensationally to give himself a chance of a poidum finish while Max Verstappen has gone from last (after a puncture) to 10th and in the points.
Ricciardo has nipped past Raikonnen, he's up to 4th. Brilliant stuff from the Aussie.
Here's a visual demonstration of Mercedes' absolute dominance.
Australian Ricciardo has been the real star today. He's risen from 16th to 5th. His Red Bull team have just told him over the radio that: "Vettel is a bit slow, I think you can catch him."
Hamilton has gone in to swap his supersofts for some soft compounds. Bottas leads, almost certainly temporarily. But further back, Verstappen is flying through the field.
Vettel now nearly 20 seconds back on Hamilton. If Bottas can hold on to second, Hamilton will take the championship lead.
It's already looking like Hamilton's to lose here. The only minor complication is that he's yet to pit.
Lap 17 of 53
We're starting to see some early pit stops now, including Force India's Esteban Ocon, who started the race in second. Ricciardo is having a stormer, he's up to fifth now - up 11 places.
Lap 15 of 53
It's all looking fairly set up, even at this early stage. The Ferraris just don't seem to have the pace to keep up with Hamilton.
Lap 10 of 53
The Mercedes drivers dominating from the front now, with Hamilton nearly three seconds ahead of teammate Bottas, who has recorded the fastest lap so far. The Brit is now 10 seconds up on Vettel.
Lap 7 of 53
Here's how we're looking early on...
Lap 4 of 53
Big trouble for Verstappen. The young Red Bull driver got off to a flyer, making up several places, but seems to have got a puncture after an incident involving Massa. He comes out of the pits in last place.
Lap 3 of 53
A little further back in the field there was an interesting little tussle between Bothas and Raikonnen. The Finn tried to take his rival out early but Bothas edged back in front.
Lap 1 of 53
We're off! A relatively uneventful start, with Hamilton maintaining his lead.
Conditions looking set fair for this 53 race lap. Interestingly, the lap record for Monza was set way back in 2004 by Rubens Barichello. Can anyone threaten the 1.21:046 time today?
We're moving towards the business end of the season now, with today's Grand Prix at Monza the 13th race of 20. After his record-breaking pole position yesterday, Lewis Hamilton will be confident of cutting in further to Sebastian Vettel's seven point lead, especially with the German down in 8th.
However, the forecast is for dry weather, which doesn't neccessarily play to the British driver's strengths. We'll see in about half an hour.