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Immobile gave away a penalty in the fifth minute which was converted but made amends by equalising at the start of the second half for his 29th league goal in as many appearances this season before Marco Parolo gave the visitors another gutsy win.
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Second-placed Lazio, who hit back to beat Fiorentina 2-1 on Saturday, have 68 points from 29 games, one behind reigning champions Juve who were playing at Genoa later on Tuesday.
"The team showed a spirit of sacrifice, especially the attackers," said Lazio assistant coach Massimiliano Farris, standing in for Simone Inzaghi who was suspended after being sent off in their previous game.
We built well throughout the game and our quality came through. We've overturned two hazardous games which weren't easy. The lads are up for it, especially from a mental point of view.
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The only sour note for Lazio was a yellow card for Immobile, who will miss their next game against AC Milan to end his ever-present record.
Immobile, who ran tirelessly for the whole match, was initially the villain when Nicolas Nkoulou's header hit his outstretched arm and Torino captain Andrea Belotti gave the hosts an early lead from the spot.
The 30-year-old forward also wasted a chance to level in the 22nd minute when he fired over from Sergej Milinkovic-Savic's pass as the visitors penned Torino back in their own half.
Lazio defender Francesco Acerbi had a goal chalked out for offside just before halftime but Lazio finally broke through two minutes into the second half when Immobile equalised with a clinical finish from Luis Alberto's incisive pass.
They kept pressing relentlessly and were rewarded in the 73rd minute. Milinkovic-Savic saw a shot blocked by goalkeeper Salvatore Sirigu but Torino failed to clear the ball properly and it fell to Parolo who scored with a deflected shot.
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