Six years after Arsenal's last appearance in the competition, Arsenal scored through Bukayo Saka, Leandro Trossard and Gabriel Jesus before the break, and captain Martin Odegaard in the 70th minute.
Saka, making his debut in the competition, like many other Arsenal players, scored from close range eight minutes later, and Trossard added the second with a powerful ground shot, before Jesus ensured the hosts' victory.
Arsenal, who have picked up 13 points from the first five Premier League games, will play at Lens in the next round of the Champions League, while PSV Eindhoven will try to recover against Sevilla.