The visitors made the breakthrough four minutes from time through Arturo Vidal, prompting a frantic final few minutes at Turin's Stadio Olimpico.
Torino defender Kamil Glik was sent off for a second bookable offence in the 90th minute, with Claudio Marchisio then grabbing a stoppage-time goal to seal the away win.
With just 12 points left to play for, the result moved Antonio Conte's side 11 points clear at the summit.
Behind them, AC Milan regained third spot from Fiorentina by twice recovering from a goal down to get the better of Catania with a 4-2 win at the San Siro.
Nicola Legrottaglie headed the visitors in front on the half-hour mark, only for Mathieu Flamini to equalise on the stroke of half-time.
Gonzalo Bergessio restored the Sicilians' lead on 65 minutes, but two goals in four minutes from substitute Giampaolo Pazzini turned the game in the Rossoneri's favour before a late Mario Balotelli penalty sealed matters.
Adem Ljajic starred as Fiorentina cruised to a 3-0 victory away to Sampdoria, who played the last 10 minutes of the game a man short following the sending off of Daniele Gastaldello.
Ljajic scored the second just before the break, adding to Juan Cuadrado's opener, before setting up Alberto Aquilani for the third.
Siena's relegation worries increased as Pablo Osvaldo's hat-trick helped European hopefuls Roma to an emphatic 4-0 victory at the Stadio Olimpico.
Osvaldo netted twice in the first half, with Erik Lamela on target in between, and then completed his treble midway through the second period.
The result lifted Aurelio Andreazzoli's side to fifth in the standings, while Giuseppe Iachini's side slumped to 19th following wins for fellow strugglers Palermo and Genoa.
Lazio are three points off the last Europa League spot for next season after a goalless draw with Parma at the Stadio Ennio Tardini.
Palermo moved out of the relegation zone and dealt Inter Milan's hopes of European football next season a blow with a hard-fought 1-0 win.
Josip Ilicic scored the only goal of the game after only 10 minutes to lift the hosts out of the bottom three on goal difference. Defeat left Inter in seventh, two points off a Europa League place.
Genoa picked up three crucial points in their battle against relegation with a narrow win at Chievo.
Davide Ballardini's men came to life in the second half with Marco Borriello scoring the only goal of the game in the 74th minute to take the Rossoblu out of the bottom three thanks to Roma's win over Siena.