The first French race winner in 24 years seized his opportunity and resisted late pressure from Carlos Sainz of McLaren to claim his team’s second victory with Lance Stroll finishing third for Racing Point.
“It was such a crazy race,” said Gasly.
It was the Alpha Tauri outfit’s second win on Italian soil – the first having been scored for them when they raced as Toro Rosso by Sebastian Vettel, his maiden F1 win in a rain-hit race in 2008
Pole sitter Lewis Hamilton was on his way to a comfortable win before a 10-second stop-go penalty for taking a pit stop when the pit lane was closed, pushed the Mercedes world champion to the back of the pack.
The six-time champion eventually ended up in seventh place.
Gasly, who was dropped by Red Bull to rejoin the junior sister team last year, jumped for joy as he leapt from his car, was the first French driver to win a Grand Prix since Olivier Panis was triumphant at the 1996 Monaco Grand Prix.
“Honestly, it’s unbelievable,” said the 24-year-old from Rouen.
“I don’t think I’m realising what’s happening right now. We’ve been through so much in the past 18 months. I have no words.”
The Ferrari-bound Sainz said he was “halfway disappointed” with his first podium finish.
“You wouldn’t believe I would have a chance at victory, but in a normal race I think I could have finished second behind Lewis.”
Stroll said: “It’s been a couple of years since I was on the podium so it’s good to be back.”
Lando Norris came home fourth in the second McLaren ahead of Valtteri Bottas of Mercedes and Daniel Ricciardo of Renault.
Despite the penalty, Hamilton still managed to extend his record run to 41 successive points finishes.
He has a 47-point lead over Bottas in the championship.
Hamilton also had the fastest lap of the race on Sunday as he finished ahead of Esteban Ocon in the second Renault, Daniil Kvyat in the second Alpha Tauri and Sergio Perez in the second Racing Point.
Ferrari endured another torrid weekend with last year’s winner from pole position Charles Leclerc walking away after surviving a high-speed crash that led to the decisive 25-minute red-flag interruption.
Four-time champion Vettel, who is leaving Ferrari after this season, retired after a brakes failure
while Max Verstappen of Red Bull also retired with engine problems.