Roma's defeat to Fiorentina on Saturday had opened the door for the Nerazzurri to climb the table, but they failed to make their first-half dominance count as a goal from their former loanee Adem Ljajic sealed an unlikely home victory.
Luciano Spalletti's Inter were on top from the off but, after missing chance after chance, Torino took their first opportunity through Ljajic and then grew into the game.
Ljajic could well have added a second, before the visitors rallied again and fell just short of the equaliser that would have taken them up the table and closer to Champions League qualification.
Having wasted numerous openings against rivals AC Milan on Wednesday, too, Inter must hope they will not rue this week come the end of the season, with Lazio - in action later on Sunday at Udinese - hot on their heels.
The tone was set after 11 minutes when Salvatore Sirigu spilled a cross at Ivan Perisic's feet, only for the winger to send a tame lob back into the grateful arms of the goalkeeper.
Sirigu was rather more impressive with an instinctive reaction stop to turn Mauro Icardi's 12-yard volley over the top, before parrying away an Andrea Candreva strike.
The visitors kept the pressure on and Perisic's towering header from a right-wing corner clipped the crossbar.
Candreva's swirling effort tested Sirigu again and Joao Miranda's blushes were then spared by a tight offside call as he somehow smashed against the post from Icardi's knockdown.
But the opener came at the other end, Inter conceding for the first time in six matches. Perisic nudged the ball away from Andrea Belotti but inadvertently fed Lorenzo De Silvestri, who squared for Ljajic to tap into an unguarded goal.
1 - Torino have found the goal with their 1st shot on target vs Inter, while the Nerazzurri had already attempted 6 in the game without scoring. Break.— OptaPaolo (@OptaPaolo) April 8, 2018
De Silvestri looped a header onto the roof of the net at the start of the second half and the same player then looked to have doubled the lead with a clever volley over his shoulder, only for Samir Handanovic to spring away to his left and make a sublime save.
Ljajic fired across the face of goal following Cristian Ansaldi's slaloming run, before Inter belatedly responded and Nicolas Nkoulou was forced to hack Miranda's header away from the goal-line.
Rafinha cracked a shot against the foot of the post, but that was as close as Spalletti's men came and they could now slip below Lazio and out of the Champions League places.