The Sweden star scored two goals in three first-half minutes as the French league leaders ran riot at Leverkusen's BayArena in Tuesday's last-16, first-leg clash.
Bayer were reduced to ten men for the final half an hour when Ibrahimovic's marker Emir Spahic was sent off for a second yellow card.
Ibrahimovic's two goals left him as the competition's top-scorer with 10 Champions League goals in six matches, one more than Real Madrid's Cristiano Ronaldo.
This was a five-star performance from PSG, but Ibrahimovic was forthright when asked if this Parisian side was the best team he has played in.
"I've played in fantastic teams so difficult to say, you can have a great team, but not win trophies, we need to finish the job first," said the 32-year-old Ibrahimovic.
Midfielder Blaise Matuidi put PSG ahead with barely two minutes gone before Ibrahimovic netted a penalty, then added a second when he unleashed a thunderbolt of a shot to make it 3-0 at the break.
Replacement Yohan Cabaye then added PSG's fourth just before the final whistle to complete the rout. "I have an embarrassment of riches in my team at the moment," said PSG's contented coach Laurent Blanc.
"We rediscovered the football we showed in the group stages, it was better than we played at the start of the year and I was pleased to see it. The players did really well and I have to praise them for the performance.
"We didn't want to give Bayer any self-confidence and we tried to make sure they didn't get any of the ball. We kept trying to push forward even when they started getting physical trying to stop us."
Blanc dampened down growing expectations and said PSG will approach the return leg eager to secure another victory over Leverkusen, who have now lost six of their last eight matches.
"It doesn't matter how the first leg went, we still have the second to come, obviously this is a big step towards the quarter-finals, but we want to win the return at the Parc des Princes," said Blanc.
"We have ambitions in this competition. This is just one game and we can still meet other teams who have lots of experience, but of course the hopes and expectations are growing."
Having been routed 5-0 by Manchester United at the end of November in their previous home Champions League match, Leverkusen were again outgunned and outclassed on the European stage.
"In the first half, we played without motivation, with fear," complained defender Omer Toprak.
"Paris walked over us. It was too easy for them. We didn't win any 50-50 balls, we got nothing.
"Unfortunately we quickly found ourselves reduced to 10 men in the second-half, which was a shame."
Sami Hyypia-coached Leverkusen now face an unenviable task to try and salvage something from the return leg in Paris on 12 March.
"It's not easy to sit here after a performance like that," said ex-Liverpool defender Hyypia, whose team have lost their last three home games.
"We played against a good team and to be behind after just three minutes only made it harder.
"Paris showed how strong they are. In the second-half, we played better after the red card with ten men than we did with eleven."