Kieran Gibbs and Lucas Perez combined twice within the opening 16 minutes as Arsenal raced into a 2-0 lead, showing no signs of nerves as they needed to beat Basel and hope that PSG drop points at home to Ludogorets.
Perez got his first after Gibbs rolled a pass to him, leaving him to tap into an empty net.
The Spaniard's second came when Gibbs' shot was parried into his path, once again leaving him with a simple finish.
Perez completed his hat-trick less than two minutes after half-time, when he hit his third past Thomas Vaclik.
Alex Iwobi scored to put Arsenal 4-0 up, before Seydou Doumbia scored a consolation goal for the home side.
With PSG drawing 2-2 at home to Ludogorets, Arsenal top the group and will in theory, receive an 'easier' tie.
However, the Gunners could still face either Real Madrid or Borussia Dortmund in the first knockout round.