Late goals from Stefan de Vrij and Alessandro Bastoni were all the Black and Blues needed to secure a comeback victory after going down to Gervinho’s opener.
Antonio Conte’s men came into the game following a disappointing 3-3 home draw against Sassuolo on Wednesday and were hoping to take a positive result from Stadio Ennio Tardini.
However, they were pegged back by a 15th-minute strike by Gervinho thanks to an assist from Juraj Kucka.
The Ivorian coolly displaced Antonio Candreva and Danilo D'Ambrosio before slotting into the bottom-right corner of goalkeeper Samir Handanovic.
Four minutes later, Inter were handed a penalty owing to Andreas Cornelius’ handball – but a VAR check ruled against the decision as Diego Godin had been offside before the incident.
The visitors’ ambition for a comeback was looking destined to end in vain after substitute goalkeeper Tommaso Berni was shown the red card for dissent from the bench in the 69th minute - he ushered in Chelsea loanee Moses for Antonio Candreva.
That proved to be the turning point as Conte’s men levelled matters eight minutes from full-time through defender Stefan de Vrij after heading home Lautaro Martinez's header.
Victory was guaranteed three minutes later through Godin’s replacement Alessandro Bastoni who headed past Luigi Sepe to the despair of Parma who had Kucka sent off two minutes earlier.
Nigeria’s Moses who was featuring in his sixth Italian elite division game of the season got cautioned by referee Fabio Maresca in the closing stages of the game for time-wasting.
After an impressive shift, Gervinho was replaced in the 86th minute by Gaston Brugman, while Ghanaian superstar Kwadwo Asamoah was an unused substitute by the San Siro giants.
Thanks to this victory, Inter remain third in the log having accrued 61 points from 28 league games – eight points behind leaders Juventus.
They take on struggling Brescia on Wednesday, while Parma face Hellas Verona in a game that could prove key to both teams' European ambitions.