Olivier Giroud opened the scoring against his old club with a wonderful header and Pedro swept past the retiring Petr Cech from Hazard’s cross.
Having set up the second, the Belgian scored a penalty to make it 3-0.
Alex Iwobi gave Arsenal hope with a swerving 20-yard strike but Hazard smashed home Giroud’s cross to seal it.
It was a London derby low on atmosphere, 2,500 miles away from home with plenty of empty seats, and those who were there witnessed a dull first half.
But the second half burst into life with the last four goals coming in the space of 12 minutes.
Arsenal miss out on a Champions League place next season as a result of their defeat in Azerbaijan.