Ludogorets's Brazilian left back Natanael opened the scoring with a stunning free kick in the 16th minute but the visitors soon seized the initiative, enjoying more of the possession and levelled the score four minutes before the interval.
Blaise Matuidi latched on to Marco Verratti's through ball to race clear and gave keeper Vladislav Stoyanov no chance with a precise left-foot shot.
The visitors dominated after the break and Cavani, who also scored in PSG's 1-1 draw against Arsenal in their opening match, netted two times in the space of four minutes.