Pole-sitter Raikkonen looked set to win his first race in more than five years - and Ferrari's first in their homeland since 2010 - but Hamilton executed a brilliant pass on the Finn with just eight laps remaining.
The thrilling victory was a fifth in a row for Mercedes at Monza, spiritual home of the sport's most glamorous and successful team, and one of Hamilton's most satisfying.
"Unfortunately I was the one that spun around, which was a bit ironic".
Now, Vettel has fallen 30 points behind Hamilton in the championship fight.
The Italian media and others surmised, however, that Raikkonen's uncompromising start may have had something to do with other matters off the track that left him in no mood to make life easy.
"I wouldn't say it was really a miracle today I think and before the race as you can see out there, there's a lot of Ferrari fans obviously and there's a lot of that negative sound that you hear, that just encourages me, it energises me and also particularly when go around there's quite a lot of British fans around". I don't know, we touched it was a brief moment.
After calling into the pits, Vettel fought back through the field to finish fourth, partly thanks to Max Verstappen of Red Bull taking a five-second time penalty for a brush with Valtteri Bottas in the second Mercedes.
"I know I've got those individuals who are out there who travel the world to support me". "I do not think we need big changes".
"I'm really happy I've been able to extract more from the auto and hopefully make that little bit of a difference".
"Obviously it doesn't help when you lose points", he added.
Hamilton's overtaking move on Vettel was investigated by the stewards but they took no action, deeming it a racing incident. "But I'm not entirely happy with the end of my qualifying and that's the emotion that's dominating at the moment".
Vettel said the clash was a result of a sequence of events starting with the first corner and implied that his spin was partly caused by the fact he had Raikkonen in front of him, which would cost him some grip. Yesterday I was trying to figure out how aggressive you can be because my race is not really with Kimi, it's with Sebastian. However, he said that he's "not too worried" about the championship situation.
"But then what can you do when you get spun around?"
"We have Vettel who is the Ronaldo of formula one and Kimi who is a great friend".