Inter had the opportunity to apply pressure on league leaders Napoli with the first match of the round, and the home side got off to a fast start, testing the Parma goal with multiple efforts inside the opening quarter-hour, the best of which fell to Denzel Dumfries, who was denied by the woodwork from a tight angle.
Hakan Calhanoglu was next to test Zion Suzuki with a shot from the edge of the box, but the Japanese goalkeeper comfortably palmed the ball away.
Parma were on the back foot for the majority of the first half, but the visitors did have one effort on target in the opening 45 minutes after Matteo Cancellieri was played in down the left, but his shot was hit straight at Yann Sommer.
Inter kept probing though, and the opening goal duly arrived five minutes before half-time after Federico Dimarco played a slick one-two with Henrikh Mkhitaryan before poking the ball home.
Inzaghi’s men picked up right where they left off after the restart, dominating proceedings as they tried to put the contest beyond Parma.
First, Dumfries flashed a header agonisingly wide, before the hosts doubled their lead in the 56th minute.
Mkhitaryan was once again the provider, releasing Nicolo Barella and the Italian midfielder showed great composure to take a touch and slot the ball home.
The Nerazzurri showed no signs of slowing down, as Lautaro Martinez twice went close but Suzuki made a pair of strong stops. The third goal appeared inevitable and eventually arrived in the 67th minute through a player who was born in Parma.
Marcus Thuram got on the end of a flick-on from a corner, volleying home his 10th league goal of the season.
The hosts were in total control and looked to be coasting, three goals to the good.
However, Parma, who had failed to hit the target in the second half, were given a glimmer of hope with 10 minutes to go, after Matteo Darmian put the ball into the back of his own net when trying to make an interception.
However, the goal proved to be nothing but a gift and a consolation, as Inter comfortably saw out the victory to go level on points with second-place Atalanta ahead of their game tonight against city-rivals AC Milan.
A poor showing from Parma brings to an end their unbeaten run of five games on their travels.