With Antonio Conte watching on from the stands as he served a touchline ban, Gervinho's 15th-minute goal looked set to be enough for Parma to secure a valuable win in their push for Europe.
Yet Inter fought back in the closing stages – De Vrij rather fortunately turning home Lautaro Martinez's header in the 84th minute before Bastoni headed in the winner three minutes later to consolidate Inter's place in third.
Bastoni's goal came almost immediately following the restart after Inter's equaliser, with Juraj Kucka's dismissal for dissent having caused a lengthy stoppage.