Inter were hoping to pick up where they left off before the international break, going unbeaten in their opening five games, and the Nerazzurri got off to a rapid start and netted twice inside 20 minutes.
First, Petar Sucic opened the scoring as he took advantage of a blunder at the back when Parma goalkeeper Edoardo Corvi passed to Mandela Keita on the edge of the box, but the Croatian midfielder won the ball and powered in off the post.
The hosts doubled their advantage five minutes later after Diego Carlos was penalised for fouling Pio Esposito in the box, and following a check with the pitchside monitor, a penalty was awarded.
Hakan Calhanoglu stepped up to fire his penalty into the bottom-left corner for his third strike in Serie A this season.
Cristian Chivu’s men were relentless and netted a third goal on the half-hour with a swift move from defence into attack.
Henrikh Mkhitaryan sent Marcus Thuram through on goal, and the French striker showed great composure to fire across Corvi into the far corner.
The Nerazzurri picked up where they left off following the restart and came close to netting a fourth minutes into the second half when Thuram fed Federico Dimarco on the overlap and his low drive into the danger area was turned goalward by Esposito but he was denied by the feet of Corvi.
Parma threatened in a rare foray forward but Mariano Troilo headed high and wide - summing up the visitors’ poor evening.
Inter remained in control of the contest as time was running out with little trouble from the away side as Chivu’s men coasted through to secure a fifth win in six league games (D1) while Parma suffered fourth defeat in as many matches (W1, D1).
Flashscore Man of the Match: Carlos Augusto (Inter Milan)