While Vettel's victory at the Belgian GP two weeks ago was clinical, Sunday he was forced to overcome a difficult start from the pole position and gearbox trouble to beat Ferrari's Fernando Alonso and Red Bull teammate Mark Webber.
"The heartbeat was a bit higher in the car and also the pit wall, because we didn't know what was going on," Vettel said about the gearbox problem. "I tried to pace myself a little bit more and control the gaps."
Before the race, Ferrari team principal Stefano Domenicali gave Alonso two races — the next is Singapore in two weeks' time — to close the gap before the team switches its focus to developing next year's car.
Alonso is 53 points behind Vettel with seven races to go and the Spaniard already sounds like he's given up. Lewis Hamilton is 81 points back in third with only 175 available.
"We didn't close the gap in the championship, which is obviously the goal," Alonso said. "We don't have enough races and we don't have the speed now to win consecutive races."
Nevertheless, Alonso drove well from fifth on the grid.
"It's a fantastic feeling here in Monza. The fourth year I have driven for Ferrari, the fourth time on the podium," he said. "Every year it's something amazing, something unique."
Vettel locked his tires on the first turn as the Ferrari of Felipe Massa pressured him from behind, but after that the German consolidated his advantage to beat Alonso by 5.4 seconds and Webber by 6.3.
"This is the best podium of the season, I'm very proud," Vettel said. "We had problems with the gearboxes at the end, but I was OK because I had a good cushion."
Monza is the home race for Ferrari fans and there were loud jeers when Vettel was on the podium.
"You can hear the difference when you don't win here in a red suit but it means you have done well and beaten the red men (of Ferrari)," Vettel said. "The more booing we get the better we've done today. I don't blame the people to be honest, it's in their genes. They love Ferrari."
It was Vettel's third career win at Monza — his first was with Toro Rosso in 2008 and then Red Bull in 2011 — his sixth of the season and 32nd overall, moving him even with Alonso's win total.
He was more emotional than usual, shaking his head vigorously in celebration and letting out his trademark high-pitched whoop as he celebrated his third win in the past four races, then pumping his fist several times as he walked up the podium steps.
Massa finished fourth ahead of German drivers Nico Hulkenberg — a season's best for Sauber — and Nico Rosberg, who was sixth on a poor day for Mercedes.
There was light rainfall before the race, but the sunshine returned as Vettel started from pole for the 40th in his career and first since the Canadian GP in June.
Roared on by thousands of flag-waving tifosi, Ferrari had a point to prove and Alonso brilliantly overtook Webber on the outside and then zoomed ahead of Massa.
After 10 of 53 laps, Vettel led Alonso by about 5 seconds, but engineers told him that his front right tire had taken some damage on turn 1 and Alonso began to make up time.
Vettel pitted on lap 24, switching from medium to hard tires, followed shortly by Webber and Massa, but Alonso stayed out until lap 28 as leading drivers chose a one-stop strategy.
In his last European race before he retires from F1 at the end of the season, Webber got his first podium at Monza.
"Good battle with Fernando," the Australian said. "Last time in Monza, so thank you very much."
Briton Paul di Resta's race lasted a few seconds after he sustained damage to the front left tire of his Force India car. He appeared to hit the back of Romain Grosjean's Lotus and stewards were investigating the incident.
Hamilton started from 12th after his worst qualifying performance this campaign and finished ninth.
"That's it for the Championship now," said Hamilton, who won the F1 title in 2008.