Choupo-Moting needlessly deflected a goal-bound shot from team-mate Christopher Nkunku onto the post from point-blank range to prevent his side going 2-1 in front in the first half.
The Cameroon striker had given PSG a 13th-minute lead but Strasbourg equalised through Nuno Da Costa and Anthony Goncalves gave the visitors the advantage before the break.
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Thilo Kehrer leveled in the 82nd minute but that was too little, too late for PSG, who until Sunday had won all of their 15 league matches at the Parc des Princes this season.
With Kylian Mbappe on the bench and Angel Di Maria, Edinson Cavani and Neymar all injured, Choupo-Moting was the only striker on the pitch and he opened the scoring after 13 minutes from inside the box.
Goncalves' stunning volley from 18 yards put Strasbourg ahead seven minutes before the break against a PSG side who had previously been behind on the scoreline for only three minutes in Ligue 1 this season.
Eric Choupo-Moting traps the ball on the goal-line
Image credit: Getty Images
Tuchel eventually sent Mbappe on the pitch to take Choupo-Moting's place and the France striker had an immediate impact, unsettling the Strasbourg defence with his devastating runs.
Dani Alves came close to an equaliser in the 69th minute, only for his spectacular overhead kick to crash on to the crossbar.
PSG made it 2-2 eight minutes from time when Kehrer headed home but despite the late efforts of Mbappe and Alves, the hosts were left frustrated. They will wrap up their sixth title in the last seven seasons if they avoid defeat at Lille next Sunday.
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