Uruguay striker Cavani found the back of the net in the first minute to hand PSG their second win in as many matches against APOEL, who are eliminated from Europe’s premier club competition.
PSG lead Group F with 10 points from four games ahead of Barcelona, who trail the French champions by one point. Ajax lie third on two points and APOEL are bottom with one.
Barca beat Ajax 2-0 away to book their ticket in the knockout phase.
“We did what we had to. It was difficult to find space against a team who came to defend,” said team captain Thiago Silva.
“There are still things to improve. Now we rest, because on Sunday we have another game that will be more difficult than this one.”
PSG coach Laurent Blanc added he had hoped his side would score more goals on Wednesday.
“We wanted more, the fans wanted more. There should have been more goals.” Blanc told a news conference.
“We would like to finish top of the group but so do Barcelona. But there is one game (against Ajax) before the Camp Nou and it will be equally important.”
APOEL had a good opportunity in the first half through Nuno Morais but they were never a threat at the Parc des Princes, even if PSG wasted almost a dozen chances in an erratic performance four days before taking on arch-rivals and Ligue 1 leaders Olympique de Marseille.
Blanc’s side were still without talismanic striker Zlatan Ibrahimovic, who has been out of action with a heel injury since September, but it was quickly forgotten.
Blanc said he was hopeful Ibrahimovic could return on Sunday to face PSG.
Cavani scored PSG’s fastest goal in the Champions League when he volleyed home from inside the box after teeing himself up from Gregory van der Wiel’s cross after 54 seconds, also benefiting from keeper Urko Pardo’s clumsiness.
It was Cavani’s fourth goal in as many games and the Uruguayan then wasted a handful of clear chances.
Morais came close to equalising shortly afterwards but he skied a close-range shot over the bar.
At the end of a swift move between Javier Pastore and Lucas, Cavani hit the post with a diving header from the Brazilian’s long cross from the right in the 18th minute.
Lucas’s low crossed shot then shaved the post after it was deflected by Pardo.
Cavani missed a golden opportunity in the 37th when he pushed the ball a little too far as he tried to dribble past Pardo in the box.
After the break, Pastore and Lucas unsettled the APOEL defence with dazzling runs but both failed to find the target.
Cavani missed yet another chance to put the game to bed with a low shot that went just wide off Pardo’s right post 10 minutes from time.
(Editing by Greg Stutchbury)