Arsenal raced into an early lead thanks to a brilliant individual goal from Nketiah, who cut inside from the left before rifling a low shot into the far corner.
Watford equalised when Mohamed Elneny was caught in possession inside his own penalty area and Philip Zinckernagel levelled from close range.
But an Arsenal team that included new signing Albert Sambi Lokonga went back in front in the second half when Lacazette scored a penalty after Ainsley Maitland-Niles was fouled.
It was three moments later when Tierney smashed home a half-volley before Azeez had the final say when he collected a short corner on the right-hand side of the Watford penalty area, shifted the ball onto his left foot and then curled a brilliant effort into the top corner.
There is a is a buzz growing around 18-year-old Azeez, who is being tipped for big things.
He has been with Arsenal since he was five years old and he is determined to make it at the club. He was heralded for his work ethic during his youth career, but he is flourishing into a complete midfielder.
Comfortable in possession, but athletic too, Azeez looks like a modern midfielder and hopes to make his mark next season.