Florenzi, introduced for Radja Nainggolan with seven minutes to play, provided the telling blow with an excellent left-footed finish that found the net with Torino goalkeeper Daniele Padelli rooted the spot.
Mattia Destro had given the hosts the lead in the first half but Torino's Ciro Immobile moved ahead of Carlos Tevez at the top of Serie A's scoring charts with an outstanding volley seven minutes after the break.
Florenzi's late heroics ensured Rudi Garcia's men would claim all three points, though, extending their unbeaten record in home league matches this season to 15 - 12 of which have been wins.
The result leaves Roma nine points clear of third-placed Napoli, who lost 1-0 at home to Fiorentina on Sunday.
Roma started well, with Miralem Pjanic particularly dangerous, and should have taken the lead in the 28th minute.
Captain Francesco Totti – making his 700th appearance in a Roma shirt – spurned a golden chance, shooting at Padelli from 12 yards.
Roma's first-half dominance was capitalised on by Destro in the 41st minute, with Gervinho the provider.
The ex-Arsenal man did an excellent job in heavy traffic to squeeze a ball through for Destro, and the forward made no mistake, sliding in ahead of Padelli to score his third goal in as many matches.
Torino responded just after the interval as Immobile's outstanding season continued, with his left-footed volley from 12 yards giving Roma goalkeeper Morgan De Sanctis no chance.
Immobile has now scored 17 Serie A goals this season.
Torino went close to claiming the lead twice, as Immobile shot just over before Alessio Cerci fired wide.
Cerci's chance came at the end of a swift counter-attack, but the forward, who chested down, saw his shot go agonisingly wide with De Sanctis beaten.
The missed chances kept on coming as Gervinho turned wide after a goalmouth scramble before Torino's Kamil Glik produced a defender's finish.
Glik really should have scored but failed to turn Jasmin Kurtic's shot, which was heading wide, into the back of the net.
And Florenzi made Torino pay, finishing a move in the first minute of stoppage time that started with Immobile giving possession away.
The influential Gervinho picked Florenzi out with an angled ball and the replacement shifted the ball onto his left foot before thrashing past Padelli to send the Rome crowd into ecstasy.
