A wonderful solo run and goal from Nicola Sansone on 75 minutes was enough to settle an enthralling end-to-end clash at the Ennio Tardini, with both goalkeepers pulling off a string of impressive saves.
The Nerazzurri have now lost their second consecutive away game and have picked up just one point from a possible nine since beating Juventus three weeks ago. The gap at the top remains four points, meaning Napoli stay second.
Samir Handanovic spared Walter Samuel's blushes in the fourth minute with a smart reflex save, after the Argentine cut out a low cross and almost turned the ball into his own net. Amauri followed up for the rebound, but it was easily dealt with by the Inter defence.
On 13 minutes, Fredy Guarin fizzed a free kick into the side netting. Later in the half, Amauri threatened again with a header from Biabiany's cross, but Handanovic was equal to it.
In the final minutes of the first half, Gabriele Paletta evaded Ranocchia to head a free kick just wide at the far post. Biabiany then went close with a speculative shot from 30 yards, before Amauri sent a header from a corner into Handanovic's gloves.
Mirante shuffled to save from Milito straight from the restart. On 50 minutes, Biabiany nodded a perfect Massimo Gobbi cross wide, with Handanovic rooted to the spot.
Jaime Valdes tried to test the shot stopper with a free kick from distance, but despite taking a deflection, the set piece was easily gathered.
Mirante thwarted Guarin once again just past the hour, turning a 30 yard drive over the bar.
Milito turned Paletta and cut into the box, but Mirante was well placed to stop a curling shot.
Parma finally broke the deadlock with 15 minutes left to play. At first, Sansone was no danger when he picked up the ball on the halfway line. Inter allowed the youngster to run at goal and he fired a low shot which beat Handanovic at his near post. It was Sansone's second strike of the season and his final contribution, as he came off for Ishak Belfodil.
Inter substitute Philippe Coutinho tried to conjure up an equaliser. He played a neat one-two with Milito, only to be thwarted by the excellent Mirante.
Handanovic prevented Parma from extending their lead when he tipped over Yohan Benalouane's bullet header from a Valdes free kick on 85 minutes. It's back to the drawing board for Andrea Stramaccioni's side.
Parma: Mirante; Rosi, (Benalouane 74) Zaccardo, Paletta, Gobbi; Acquah, Valdes, Marchionni; Biabiany, Amauri, Sansone (Belfodil 78)
Inter Milan: Handanovic; Ranocchia, Samuel, Juan Jesus; (Duncan 86) Zanetti, Guarin, Cambiasso, (Livaja 90) Nagatomo; Alvarez; (Coutinho 73) Palacio, Milito
Goal: Sansone 75 (P)