PSG were shocked by their Bulgarian counterparts and came within minutes of losing to their Group A rivals.
Ludogorets took a surprise lead through Misidjan before Cavani levelled the scoring with a bicycle kick just after the hour mark.
However, Wanderson put Ludogorets back into the lead less than 10 minutes later and the away side held on until stoppage time.
Angel Di Maria scored an equaliser in the second minute of added time, but PSG couldn't find a late winner on a disappointing evening for the Ligue 1 champions.
The draw means that PSG finish second in the group, behind Arsenal.