Inter moved into second in the standings although its title hopes are slim as league leader Juventus has an eight-point advantage with six matches remaining.
Torino remained five points above the relegation zone.
Ashley Young and Diego Godín scored shortly after the break after a howler from Nerazzurri goalkeeper Samir Handanović gifted Andrea Belotti the opener. Lautaro Martínez all but sealed the match.
Inter needed a win after two disappointing results. But it was Torino which took the lead in the 17th minute when Handanović uncharacteristically spilled a corner, allowing Belotti the simplest of