No wholesale alterations from PSG followed from the 1-1 draw against Lens which secured them the title last week, with Juan Bernat and Danilo Pereira in for Nuno Mendes and Idrissa Gueye.
The champions were off to a poor start on two minutes after a surging running from Kevin Gameiro resulted in a thumping near post finish that had goalkeeper Gianluigi Donnarumma stunned.
PSG conceded a second with ten minutes played through a smart first-time finish in the area from Adrien Thomasson from a cutback left of the area, but it was ruled out for offside.
However, the visitors were back on equal terms just over the midway mark when Kylian Mbappe ran onto a well-angled through pass from Neymar Junior and finished from close-range.
The leveller spurred PSG on right on the half-hour mark and they nearly went in front from a cleverly worked shot outside the area by Neymar, but Strasbourg goalkeeper Matz Sels parried.
It was a promising start to the second half from the newly-crowned champions with Lionel Messi having a shot blocked before Sergio Ramos applied an ambitious attempt from 50-yards out.
The Parisans remained in control and had the lead on 64 minutes when Achraf Hakimi found space in the six-yard area and steered Mbappe's pass into an unguarded net.
Mbappe then reversed roles four minutes later as a stray pass from Alexander Djiku fell perfectly for him who ran slightly forward before finding the bottom corner.
Strasbourg got a lifeline in the final 15 minutes after Marco Verratti helped a header from Habib Diallo following a corner-kick past Donnarumma, as PSG introduced Angel Di Maria for Neymar.
The Parisans struggled to cope and surrendered their lead in stoppage time when Anthony Caci arrived unchecked at the back-post to side-foot home a telling cross to leave the spoils shared.