Massimiliano Allegri ruled Juve out of the title race after their defeat to Atalanta on Sunday (AEDT), which followed a 4-0 thrashing at the hands of Chelsea in the Champions League.
But Juve hit back on Wednesday (AEDT), Paulo Dybala breaking the deadlock in the 21st minute, though he did send a stoppage-time penalty way over the crossbar.
Dybala's penalty miss was never going to prove costly, however, with Alvaro Morata having already sealed the points in the 70th minute.
Aiming to avoid a third successive defeat against newly promoted sides in Serie A for the first time, Juve started well with Dejan Kulusevski shooting just wide.
Kulusevski turned provider as Juve's pressure told in the 21st minute – Dybala exchanging a neat one-two with the winger before firing low beyond Vid Belec.
Giorgio Chiellini thought he had doubled the lead when he tucked home the rebound after Juan Cuadrado's free-kick was tipped onto the post, but he was denied a first league goal of the season following a VAR check, with Moise Kean deemed to have strayed offside.
Salernitana had a glorious opportunity to equalise when the ball broke kindly for Luca Ranieri in the 57th minute, but his effort crashed against the woodwork with Wojciech Szczesny beaten.
It proved costly as, just three minutes after entering the action, Morata was in the right place to flick home Federico Bernardeschi's low cross.
Dybala had the chance to put the icing on the cake from the penalty spot with the last kick of the game, but slipped at the vital moment and sliced his effort high over the goal.