Goncalo Ramos, Nuno Mendes and Desire Doue scored the goals for PSG in Austria as Luis Enrique's team won for the first time in this season's Champions League since beating Girona 1-0 on the opening matchday in September.
Scoring three times also allowed them to double their tally of goals so far in the competition, as PSG bounced back from defeats against Atletico Madrid and Bayern Munich in their last two outings.
The victory lifts the Ligue 1 leaders tentatively into 24th place in the 36-team standings, the last qualifying spot for the knockout phase.
They have seven points, the same number as Feyenoord, who sit behind PSG on goal difference but will have the chance to climb above the Qatar-owned club when they face Sparta Prague on Wednesday.
Portugal striker Ramos, who has just returned from over three months out injured, put Paris ahead on the half-hour mark when he stretched out a leg to turn an Achraf Hakimi knockdown over the line.
The second goal arrived with just under 20 minutes left as Doue cut the ball back from the byline for Mendes to fire in.
That ended any real doubt about the outcome, and substitute Doue then wrapped up the win late on after some great work by Hakimi.
PSG still have work to do with a huge game to come at home to Manchester City next, in January, before going to Stuttgart in their last outing.
Salzburg, meanwhile, have lost five of their six matches so far and are heading for elimination.
