Trapp stuck out a hand to save a Diego Costa header which had looked destined for the back of the net and ended up hitting the bar.
Chelsea performed well, although Eden Hazard, who chose the eve of the match to reveal it would be difficult to turn down a move to PSG, made a limited impact.
The Belgian playmaker did little to boost any potential transfer fee and was withdrawn 19 minutes from the end.
John Terry missed the trip to Paris and may have to wait for his 700th Chelsea appearance as he is a doubt for Sunday's FA Cup fifth round tie with Manchester City.
Gary Cahill and Branislav Ivanovic performed admirably in the absence of Terry and Kurt Zouma, who is out for the season with a knee injury.
Baba Rahman came into a reshuffled defence, which survived early pressure before the left-back delivered a cross which the masked Costa met, only for Trapp to somehow turn the ball on to the bar. It felt like a chance Chelsea had to take.
Lucas Moura had impressed early on and almost provided the opener for Ibrahimovic - but the Swede headed the ball into the ground.
Moura burst by three Chelsea players before he was tripped by Mikel, who was booked.
And Ibrahimovic's free-kick hit the midfielder and wrong-footed Thibaut Courtois.
Six minutes remained until half-time and Chelsea replied when Costa met Willian's corner ahead of Ibrahimovic, getting enough of a flick-on for the ball to drop for Mikel.
He finished emphatically from six yards for his sixth goal in 358 Chelsea games.
Trapp raced off his line to deny Costa early in the second half before Courtois repelled PSG time and again - only for his defences to eventually be breached for a second time.
First Courtois tipped Angel di Maria's effort over, then he blocked an Ibrahimovic shot and next he saved from Moura.
Chelsea were defending deep, inviting pressure.
Courtois denied Di Maria from a free-kick before the former Manchester United winger played a fine ball over the top for Cavani, who stayed onside before tucking the ball under the goalkeeper from a tight angle.
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