
Chilean defender Gary Medel scored the only goal of the game at the San Siro on the half-hour mark with a long-range drive which beat Roma keeper Wojciech Szczesny.
Roma, who had been top at the start of the day after five successive wins, had chances to salvage a point but were denied by a string of fine saves from Samir Handanovic in the Inter goal.
Roma's misery was compounded by a red card for Bosnia star Miralem Pjanic after 73 minutes.
In the Turin derby, Paul Pogba put Juventus in front after 19 minutes but Cesare Bovo looked to have saved a point for Torino early in the second period.
However, substitute Cuadrado, on loan from Chelsea, grabbed the winning goal which lifted Juventus into 10th spot, nine points behind Inter.
Juventus went into the match sitting in 12th place, with coach Massimiliano Allegri coming under intense pressure following some poor recent results.
For their part, the visitors who won the last time these sides met back in May -- were buoyed by the fact they entered the clash above Juve in the table for the first time since 1993.
Paulo Dybala allowed a pass from Cuadrado to run beyond him to Pogba, and
the French midfielder fired a first time effort beyond Daniele Padelli into the back of the net. AFP