Hamilton held his auto level with the Ferrari, which drifted into the side of the Mercedes and spun.
But this time, Vettel powered past Hamilton shortly after the start and never looked back. The long run to the first corner will be crucial and Vettel has no buffer between himself and Hamilton.
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After a Safety Car was required on the opening lap due to Brendon Hartley's stricken Toro Rosso on the pit straight, Hamilton overtook Raikkonen on the restart before regaining the position around the outside of the Variante della Roggia.
Ferrari's pace impressed Mercedes and Vettel's title rival Hamilton, but the German is not getting too carried away given the deficit they have had to make up over recent years.
But the pressure we have here in Monza is the same that we have in other places.
Other drivers: Valtteri Bottas claimed a maiden win in Russian Federation a year ago, while Kimi Raikkonen has podiumed in the last two races. Bottas then pitted, giving Raikkonen clear air, but his tyres were in trouble.
Hamilton: Possibly his most successful track with five wins from the last six races. He only drew alongside the Ferrari as they approached the braking zone but nailed Raikkonen around the outside.
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Back at the front, and it was Raikkonen who stopped for new tyres first.
After trimming Hamilton's overall lead to 17 points last weekend, Vettel is now focused on ending Ferrari's eight-year wait for a win at the Italian GP, where he says the track "in many ways is similar to Spa" and suited to the team.
Pushed a little harder, when asked why it wasn't Raikkonen giving him a tow, what he meant by the "we'll speak later" comment and whether his teammate will be allowed to win, the German said: "Well, first question, because we have an order that changes every weekend and this weekend it was Kimi to go second".
"And then there will be tracks where we are definitely the challenger, like Singapore, and maybe Mexico".
Grosjean just held on to claim sixth for Haas, with Esteban Ocon beating a charging Sergio Perez - who started 14th - to seventh.
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And having struggled latterly during his time in Spain, quickly adapting to the Premier League was never going to be an easy task. As long as Howe remains in charge, there is no reason why Bournemouth should think they have hit their ceiling.
"It's a special place for sure to get the pole position at our home grand prix in front of our fans.it's good today, hopefully tomorrow it's very good, " Raikkonen added.