Choupo-Moting, who had scored the opener, gently nudged the ball onto the post before it was cleared in what finished a 2-2 draw.
Without many of its star players, the Parisian club dropped points at home for the first time this season.
PSG would have wrapped up a sixth league trophy in seven seasons with a win but instead needed a late equaliser from Thilo Kehrer to avoid an embarrassing loss. PSG has a 20-point lead over Lille and will be crowned next week if it beats its northernrival away.
Despite the absence of injured forwards Angel Di Maria, Neymar and Edinson Cavani, PSG coach Thomas Tuchel left star striker Kylian Mbappe on the bench to start with Choupo-Mouting instead.
Strasbourg coach Thierry Laurey opted for a very defensive side that struggled to string passes together and rarely took the ball out of its own half during the first 20 minutes.
In an eventful game, Choupo-Moting put the hosts ahead in the 13th minute when Colin Dagba beat the off-side trap down the right side to deliver a precise cross for the Cameroon international, who scored with a calm finish.
PSG could not hold onto its lead for long, though, as Strasbourg gradually got into the match to find space between the Parisian lines. Nuno Da Costa made the most of a quick counter-attack ignited by Lionel Carole down the left flank to level in the 26th with a precise shot from inside the box.
After Choupo-Moting's blunder, Strasbourg kept pushing and earned a corner kick in the 38th that PSG defenders failed to clear properly. Waiting outside the box, Anthony Goncalves calmly walked toward the ball and hammered it back to silence the Parc des Princes with a powerful strike that left goalkeeper Gianluigi Buffon stranded.
Tuchel was sent off 12 minutes into the second half for an outburst of anger that followed a dangerous tackle from Kenny Lalaon Nkunku. Choupo-Moting left the pitch soon after to make way for Mbappe in the final half-hour.
The France international threatened immediately with a series of dribbles on the right side of the box as PSG accelerated the pace in search of an equaliser. He created danger on the other side of the area a few minutes later but his effort was stopped by Strasbourg 'keeper Matz Sels.
Daniel Alves then hit the crossbar with a right-footed volley and Kehrer finally snatched the equaliser from a corner in the 82nd minute when he planted a header into the back of the net after being left unmarked.
But this match will be remembered for the first half howler, despite the villain's post-match attempt to down play his blooper.
