This is the Italian team’s first win since 2008, when Sebastian Vettel took victory at Monza back when the constructor was known as Toro Rosso.
Carlos Sainz finished in second position and Racing Point driver Lance Stroll rounded out the podium.
Sainz was gaining on Gasly in the closing laps and crossed the finish line just a few tenths behind the Frenchman.
Teammate Lando Norris also put in a strong performance, finishing P4 in his Mclaren.
Meanwhile, Mercedes drivers Valtteri Bottas and Lewis Hamilton finished fifth and seventh, respectively.
Hamilton was on course to record a comfortable victory but things went south when he was awarded a 10-secon stop-and-go penalty for entering the pitlane while it was closed.
Alfa Romeo’s Antonio Giovinazzi was also awarded the same penalty for changing tyres on the same lap as Hamilton.
Race control elected to close the pitlane as Kevin Magnussen’s stricken car was being pushed by marshals back to the Haas garage.
Neither Ferrari finished the race, with Sebastian Vettel retiring due to a brake failure and Charles Leclerc crashing his SF1000 into the tyre barrier at the Parabolica.
This brought the red flag out, as the tyre barrier needed to be repaired.
Red Bull Racing failed to score a single point at Monza, with Max Verstappen having to retire his RB16 due to a mechanical issue and Alex Albon only managing P15.
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