The tall Swede opened the scoring from the penalty spot, Thiago Silva netted on his debut, Alex made it 3-0 just past the half-hour mark and Javier Pastore wrapped up the victory with a fourth in stoppage time to delight the home fans.
The French club, who have spent over 200 million euros on players since being taken over by Qatari investors over a year ago, were never really threatened by the visitors who got a late consolation through Miguel Veloso.
"It is very important to win the first game," coach Carlo Ancelotti told a news conference.
"We played a very good game, with a lot of intensity. We did a good job, it was a great night."
His Kiev counterpart Yuri Semin, who was fuming, added: "You cannot play like this at this level. We struggled on set pieces. The defensive midfielders did not do their job."
PSG next visit Porto, who won 2-0 at Dinamo Zagreb, in two weeks' time and if they put on a similar display Ancelotti's side will be a tough nut to crack.
They stamped their authority on Tuesday's game early on and never released the pressure, with Ibrahimovic and Argentina forward Pastore always looking dangerous as they benefitted from Marco Verratti's outstanding work in midfield.
Jeremy Menez was fouled in the box in the 18th minute after breaking down the left flank and Ibrahimovic coolly converted the resulting penalty.
HUGE ROAR
The striker almost doubled the tally in the 29th when he connected with a brilliant long pass from Menez. He tripped but got back on his feet only to be denied from close range.
A minute later, however, Silva found the back of the net when he poked the ball home from a poor clearance.
PSG had the points in the bag long before halftime as Alex volleyed home from a corner in the 32nd minute triggering a huge roar in the Parc des Princes.
Pastore was a permanent threat, repeatedly skipping past challenges to open up space for Menez and Ibrahimovic.
The Swede, who has settled in quickly after joining from AC Milan during the close season, came close to scoring again on the stroke of half-time but his shot was too weak.
Ibrahimovic, who now has six goals in five appearances for PSG in all competitions, was replaced 17 minutes from time by Argentine forward Ezequiel Lavezzi and was soon followed off the pitch by Silva, who got a standing ovation.
Kiev pulled a goal back in the 87th when Veloso's inswinging cross from the right drifted past everyone into the net but Pastore rounded off a comfortable night for PSG with a left-foot strike from the edge of the box that deceived the keeper.
