The Sweden international scored twice - one a stunning effort from 18 yards - to effectively end the tie after the first leg.
The Ligue 1 champions were favorites going in after an almost faultless group stage campaign, and duly backed up that billing with a commanding victory in Germany on Tuesday.
And it was Ibrahimovic who played the starring role, as he scored twice to become the top scorer in this season's Champions League with 10 goals in just six matches.
His two strikes were sandwiched in between Blaise Matuidi's opener and Yohan Cabaye's first goal for the club in the dying stages, as PSG took complete control of the tie ahead of the second leg on March 12.
Laurent Blanc's side was once again without the injured Edinson Cavani, but his absence did not appear to have any effect, as PSG took the lead inside three minutes.
Matuidi scuffed an effort under Bernd Leno to give PSG a crucial away goal after latching on to a precise pass from Marco Verratti.
Leno was perhaps at fault for the opener and almost handed the visitors a second when he spilled Gregory van der Wiel's deep cross, only for Mehmet Toprak to spare his blushes by blocking Ibrahimovic's point-blank effort.
Leverkusen looked to have stemmed the tide as chances became few and far between, however, the hosts' task was made even tougher on 38 minutes when PSG was awarded a penalty.
Emir Spahic was adjudged to have pulled down Ezequiel Lavezzi, enabling Ibrahimovic to step up and fire the spot-kick into the bottom corner.
Hyypia's men may have felt aggrieved by that decision, but could have few complaints as Ibrahimovic effectively ended the tie with a spectacular second.
Matuidi was involved again as he laid the ball off to the Sweden striker, who lashed a fierce left-footed strike from the edge of the area beyond the helpless Leno and into the top corner.
Leverkusen made two changes at the interval as Julian Brandt and Stefan Reinartz replaced Simon Rolfes and Son Heung-Min.
However, the alterations had little impact and PSG looked to have added a fourth when Matuidi's effort was deflected into the net by Spahic on 66 minutes.
That strike was ruled out for offside, but the French outfit did apply the gloss to a magnificent team display when substitute Cabaye drove home his first goal for the club from Lucas Moura's lay-off two minutes from time.