Substitute Thilo Kehrer headed in an 82nd-minute equaliser but Strasbourg spoiled the party plans in the French capital, picking up an unexpected point to keep the champions-elect waiting.
After nearest rivals Lille were only able to draw 1-1 at Reims earlier on Sunday, PSG knew three points at the Parc des Princes would see them crowned league winners for a sixth time in seven seasons.
Thomas Tuchel's side appeared on course to get the job done when Choupo-Moting tapped in Colin Dagba's low cross to open the scoring in the 13th minute, but Strasbourg had clearly not read the script.
They equalised through Nuno da Costa - who turned in Lionel Carole's low cross - before Anthony Goncalves put the Coupe de la Ligue winners ahead, smashing in a long-range drive with his right foot.
Kylian Mbappe was summoned from the bench early in the second half by Tuchel but it was another replacement in Kehrer who levelled the score, turning in Julian Draxler's corner from the right.