A run of five defeats from six games had seen European hopefuls Parma tumble down the Serie A table in recent weeks and Roberto Donadoni's men were down in 15th place on Sunday, albeit temporarily, when Mario Santana opened the scoring in the 56th minute.
That goal inspired something in a wounded Gialloblu side and Amauri made the most of a mistake from Angelo Ogbonna to level before Nicola Sansone fired Parma ahead with 10 minutes remaining.
The floodgates were open and Amauri, who had missed a host of solid chances in the first half, found time to claim to the match-ball with a well-taken double at the death.
Parma started with promise and Jonathan Biabiany almost capitalised on a lapse in concentration from visiting keeper Jean-Francois Gillet, who was caught recklessly dribbling the ball outside of his area.
Rolando Bianchi then enjoyed a fine chance at the other end, with Antonio Mirante just managing to smother after Valter Birsa had released the former Manchester City striker in the final third.
Amauri bamboozled Kamel Glik to burst past the Torino defender and test Gillet with a firm drive before Santana tried his luck against Mirante with a dipping right-footed drive.
Bianchi continued to provide a threat on the counter-attack and, after beating Gabriel Paletta in a footrace, his swift effort caused another moment of real concern for Mirante.
The five minutes before the break would belong to Parma alone as Gillet struggled to keep his side in it.
First, the Belgian anticipated Alessandro Lucarelli's clever dummy when the Parma defender had collected the ball from a corner, before improbably punching Amauri's remarkable bicycle kick off the line and to safety.
From the resulting corner, however, Gillet slightly misjudged his exit and it fell to Danilo D'Ambrosio to scramble back and clear Amauri's header off the goalline.
There was a touch of deja-vu as play resumed with Gillet forced to repel another Amauri header from a Djamel Mesbah corner, but it would be Torino who broke the deadlock.
Birsa had been key to unlocking Parma's defence in the first half and he came through again in the 56th minute as Santana defied the offside flag to collect his low cross and slot home.
It might have been much worse for Parma had Bianchi's tap-in stood two minutes later. Birsa had pulled the strings once again but the flag went up for Bianchi as he pulled the trigger.
The Torino duo pressed on, though, and it took a decisive stop from Mirante to deny Bianchi at the end of a fluid counter-attack orchestrated by Birsa.
An under-siege Parma side eventually carved out another half-chance, with Mesbah heading a rebound high over the bar, and that show of defiance allowed Amauri in for the equaliser.
With 77 minutes on the clock, the former Juventus striker telegraphed Ogbonna's interception to turn a Massimo Gobbi cross beyond the stranded Gillet.
Parma would complete their unlikely turn-around to effectively win the game three minutes later. This time Gillet stood frozen to his line as Sansone twisted his body to turn home a precise right-footed shot.
If Amauri's leveller had gone some way to atoning for his wasteful first-half performance then he was certainly forgiven as he made the points safe in the dying minutes.
First, he held off three defenders to beat an onrushing Gillet before making no mistake with a slide-rule pass from substitute Raffaelle Palladino as the Tardini erupted.