Grealish, the British record £100m signing from Aston Villa, illuminated Etihad Stadium after cutting inside from the left before curling home to make it 4-2.
Koya Kitagawa's strike just after the restart dampened the mood at the Emirates Stadium for a brief moment, but substitute Emile Smith-Rowe sent the fans home happy as Arsenal kept up their 100 per cent record in this season's Europa League.