Hamilton held his vehicle level with the Ferrari, which drifted into the side of the Mercedes and spun.
Vettel's auto slid into Hamilton's in the middle of the chicane and he spun in front of the pack, his front wing broken. The long run to the first corner will be crucial and Vettel has no buffer between himself and Hamilton.
As the laps ticked by, though, Raikkonen's older tyres began to give up, enabling Hamilton to get closer and closer, until on lap 45 the Mercedes went for the outside of the first chicane and pulled off another excellent pass.
As Q2 began, Hamilton took the initiative with a flier in 1:19.798 before Vettel did 1:19.785, an advantage of just 0.013 seconds.
Asked about his "we'll speak later" comment at the press conference, Vettel was giving little away.
Bottas eventually pitted at the end of lap 36, leaving Raikkonen and Hamilton to battle for the lead.
Other drivers: Bottas and Raikkonen share one win each in Abu Dhabi, and are likely to finish on the podium at the season-ending race.
Hamilton: Possibly his most successful track with five wins from the last six races.More news: After "Lifeless" Comment on Buhari, Trump meets with Kenyan President
Vettel leaves Monza 30 points adrift of championship leader Hamilton on a weekend where he would have expected to slice the deficit to at least 10.
And with eight races to go in the championship, we take a look at the success and form of both drivers at the remaining circuits.
Other drivers: Verstappen scorched to victory past year, while Bottas delivered podium finishes in 2015 and 2017.
Lewis Hamilton took third spot on the grid and will be followed by his own teammate Valtteri Bottas.
That allowed Vettel, who stopped again in his fightback to fifth on-track, to sneak within five seconds of the Red Bull and salvage another two points. "We can do our best only and then see what happens".
Grosjean just held on to claim sixth for Haas, with Esteban Ocon beating a charging Sergio Perez - who started 14th - to seventh.
Big news of the weekend was that billionaire Lawrence Stroll, father of Williams driver Lance Stroll, has bought the beleaguered team of Force India with the obvious intent of moving his son Lance to lead the team. It's Italy, it's special, it's our home grand prix.
Fernando Alonso was next to drop out as he limped back to the pits with a mechanical issue, before Daniel Ricciardo - charging through the field behind Vettel after starting from the back - pulled off with smoke coming from the rear of his Red Bull.