The French champions were considered favourites going into the tie after an almost faultless group-stage campaign, and duly backed up that status with a commanding victory at the BayArena on Tuesday.
And it was Ibrahimovic who played the starring role, scoring a brace to become the top scorer in this season's Champions League with 10 goals in just six matches, while Yohan Cabaye capped things off in the dying stages with his first goal for the club following his move from Newcastle United.
Blaise Matuidi gave PSG the lead almost immediately following the kick-off, before Ibrahimovic put Laurent Blanc's side in command with a confident penalty.
Leverkusen rarely threatened in a one-sided affair, the highlight of which came three minutes before the break when Ibrahimovic added another stunning strike to his portfolio of special goals.
Cabaye completed the rout late on after coming off the bench, and Sami Hyypia's team now face a near-impossible challenge in the return leg at the Parc des Princes on March 12.
PSG were once again without injured striker Edinson Cavani, but his absence did not appear to affect them, as they went ahead inside three minutes through Matuidi.
The France international scuffed an effort under Bernd Leno to give PSG a crucial away goal after latching on to a precise pass from midfield cohort Marco Verratti.
Leno was perhaps at fault for the opener and almost handed PSG 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 were 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-right 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 curled home from Lucas Moura's lay-off two minutes from time.
