Perez, making only his fifth start since joining from Deportivo La Coruna for around 17 million pounds ($US21.55 million) in August, struck twice from close range inside the opening 16 minutes.
He netted again two minutes after the break to become only the sixth Arsenal player to score a hat-tick in the competition.
Alex Iwobi made it 4-0 after 53 minutes and it could have been even better for Arsenal as Alexis Sanchez rattled the crossbar with a fizzing free kick.
The St Jakob-Park crowd finally had something to warm them on a cold night when substitute Seydou Doumbia flicked in a consolation after a skilful turn in the area.
Arsenal topped the group because PSG were surprisingly held 2-2 at home by Bulgarian side Ludogorets, who qualify for the Europa League at the expense of Basel.
