For AlphaTauri, it was the team's first success since Vettel won for the team in 2008 when it was known as Toro Rosso - also on home soil at Monza - and sadly with no Italian fans able to celebrate.
Behind the Frenchman was a remarkable podium as Carlos Sainz was second for his best result in F1, with Lance Stroll third for his first top-three finish since his maiden campaign in 2017, and first since he joined Racing Point last season.
Astonishingly, it was the first time in 146 races - since Kimi Raikkonen's 2013 win with Lotus in the season-opening Australian Grand Prix - that a Mercedes, Ferrari nor Red Bull did not take the chequered flag.
With Hamilton cruising to what would have been his 90th career victory, the nature of the race altered markedly on lap 20 due to Kevin Magnussen sustaining a failure on his Haas that resulted in him pulling off the track at the entry to the pit lane.
Given the position of Magnussen's car, and the fact it could not be retrieved safely, it meant FIA race director Michael Masi was forced to deploy the safety car and close the pit lane.
Hamilton, though, pitted as both the Briton and his team missed the flashing signs at the side of the circuit through the Parabolica and the FIA notification. Alfa Romeo's Antonio Giovinazzi also pitted.
During the safety car period, the FIA soon handed Giovinazzi a 10-second stop-go penalty as his infringement was blatantly obvious giving the timing of his pit stop in relation to when the pit lane was closed. Hamilton's was less clear initially.
When the pit lane reopened, and the remainder of the field opted to change tyres - with the exception of Stroll - it shook up the order behind Hamilton.
Further drama, though, unfolded on the first lap after the safety car had peeled away, with Leclerc hurtling off at Parabolica and ploughing heavily into a tyre barrier, ultimately leading to the race being red-flagged.
Such was the severity of the crash, and the time required by the FIA and marshals to carry out barrier repairs, the cars all returned and lined up in the pit lane, and with the drivers allowed to leave their cars.
Soon after stepping out of his Mercedes, Hamilton was also given a 10-second stop-go penalty, which led to an intense debate between the Briton and his team on the pit wall.
A clearly frustrated Hamilton opted to use the time to visit Masi, likely to understand his reasoning for the penalty, but it proved to no avail.
After a 27-minute hiatus, the drivers then lined up for a second formation lap, and with 26 laps remaining, effectively resulting in a sprint race, albeit with Hamilton and Giovinazzi needing to take penalties.
The grid was a fascinating one, though, as behind Hamilton it was Stroll, Gasly, Alfa Romeo's Kimi Raikkonen and Giovinazzi, followed by Sainz, McLaren team-mate Lando Norris and Valtteri Bottas who had struggled from the start in his Mercedes, losing four places on lap one as he dropped from second to sixth.
Although Hamilton argued beforehand as to when to take his punishment, he was told to "suck it up" by his team and simply get on with it.
It led to Hamilton taking the penalty after the first new lap, understandably dropping him to last of the 17 runners, and dropping him to 28 seconds behind Red Bull's Alex Albon in 16th.
Hamilton was soon 15th, though, as Giovinazzi pitted for his penalty, while Verstappen's run of six consecutive podiums ended with retirement.
While Hamilton made his way through the field, out front it became a battle between Gasly and Sainz for the win, with the Spaniard slowly creeping up to the rear of the AlphaTauri.
On the last lap, Sainz dumped his McLaren's battery in a bid to snatch the win, but it was to no avail as he finished just 0.415secs behind Gasly, making him the first French winner of a race since Olivier Panis in the 1996 Monaco Grand Prix.
Stroll took third ahead of Norris, with Bottas fifth, Renault's Daniel Ricciardo sixth, with Hamilton seventh, and with him taking the point for fastest lap given his remarkable charge from the rear.
It means Hamilton has at least equalled another record of Michael Schumacher as it was his 221st career points finish, while it also equals Nick Heidfeld's record of 41 consecutive classified finishes set from 2007 to 2009 while the German was with BMW Sauber.
On a dismal day for Ferrari, Vettel retired with brake failure after just six laps.
Initially informed from the pit wall he had an issue, and as television images showed a part of his car flying off along the long straight that leads into the Parabolica, a fire soon materialised with the left-rear brake.
Heading into lap six, the four-time F1 champion was forced to plough through the polystyrene blocks at the first chicane before slowly returning to the garage where he retired for the second time this season.
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