Juan Pablo Montoya made the breakthrough at Monza
The Colombian started three of the last four races from pole position but was not able to convert those performances into a win until Monza.
A repeat looked on the cards when he saw his early lead disappear as Ferrari's Rubens Barrichello went ahead after the pit-stops.
"For being my first year I wasn't really expecting to win and I thought if the time is meant to come for me it will come," said Montoya.
"I have had a lot of bad luck. My luck was about to change and it did. The last four races I have had three pole positions so we will see what happens.
"This is a big day for me. I'm delighted to have won, particularly because my father is here."
Barrichello put in a strong performance to take second, pulling off the best manoeuvre of the race when he passed Ralf Schumacher on the first lap.
"He (Schumacher) was struggling with the brakes, especially on turn one, and when I was on the inside I thought I would brake a little bit earlier and go through," said Barrichello.
But the Brazilian was downbeat after the race in the light of recent events in America and the Cart series crash on Saturday that left Alex Zanardi in a critical condition.
"There was something going on behind us and this weekend has been very dark, not only for the United States but also what happened to Zanardi yesterday," said the Ferrari driver.
Zanardi was a Williams driver in 1999 and team boss Frank Williams admitted it had been hard to focus on the race after hearing about the Italian's crash in Germany.
Respect
He said: "Everyone in the team is devastated by the news of Alex's serious accident. Our thoughts and prayers are with him and his family.
"He is a true gentleman and I know his many friends and fans round the world will have him in their thoughts and be hoping for good news about his condition."
All the drivers apart from Jacques Villeneuve agreed before the race not to overtake in the first two chicanes as a mark of respect, but team bosses insisted they drive as normal.
Barrichello was not impressed by the Canadian driver's attitude.
"It is bad when you have an agreement and one guy doesn't want to do it," said the Brazilian. "That is pretty much life."
Montoya added: "We tried to do an agreement and we couldn't. Everyone was pretty reasonable about the start."
Scotland's David Coulthard was in fifth before retiring with a mechanical failure early on, but he holds on to second place in the championship ahead of Barrichello.
"I was never going to be in a position to race with the Ferraris or the Williams," Coulthard admitted.