The volatile Sweden striker, who took his tally in this season's competition to 10, also converted a penalty after Blaise Matuidi had given the French side an early lead.
Yohan Cabaye added the fourth two minutes from time and Leverkusen, beaten 5-0 at home by Manchester United in the group stage, had no answer to PSG's slick passing as they slumped to another heavy defeat.
The Bundesliga sides's misery was increased when defender Emir Spahic was sent off in the 59th minute for a second yellow card.
- Sports & Recreation
- Yohan Cabaye
- Blaise Matuidi
- Manchester United