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.
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.
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.
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.
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.
