Nacer Chadli netted a vital away goal for the visitors shortly before the interval before Federico Bernardeschi profited from a deflection off the tip of Ryan Mason's boot to restore parity.
The visitors began very assured in possession with Dele Alli waltzing past a pair of Viola defenders inside the danger area to soothe the travelling supporters’ nerves.
Fiorentina, though, seemed perfectly content in allowing Spurs to hoard possession, the introduction of Mauro Zarate to the starting XI after his dismissal against Inter on Sunday evening, equipping the home side with a potent threat on the counter-attack.
Almost 17 minutes had elapsed before either side fashioned a shot in anger.
Zarate, occupying a similar position to the one which yielded euphoria against Carpi earlier in the month, drifted inside but curled his effort over the crossbar.
Kevin Wimmer expertly intervened when Borja Valero slid a delicious pass through to Josip Ilicic five minutes later.
Christian Eriksen unleashed an arcing effort towards the Fiorentina goal but Ciprian Tatarusanu did well to assess the flight of the Dane’s attempt and claw the ball over the crossbar.
Few could believe just how Federico Bernardeschi squandered the hosts best chance of the half when he ghosted in-behind Toby Alderweireld and failed to make sufficient contact with Ilicic’s unerring delivery to the far stick.
The complexion of the tie altered nine minutes from the interval, however, when Nenad Tomovic upended Ben Davies inside the danger area.
Nacer Chadli, spearheading the away side’s attack on the evening, spotted the penalty and sent Tatarusanu the wrong way to register his side the all-important away goal.
Zarate spurned the chance to restore parity on the stroke of half-time when he ballooned Kuba Blaszczykowski's deft cut-back over the bar.
Heung-Min Son thought he had doubled his side’s advantage within sixty seconds of the restart when he nodded Eriksen’s free-kick beyond Tatarusanu. The linesman, though, adjudged the forward to have strayed offside.
Wimmer foiled Zarate impeccably at the near post after Marcos Alonso picked out the nimble attacker inside the danger area.
Spurs carved their guests open yet again on 54 minutes when Chadli was ushered in by Moussa Dembele. Opting to take the ball on his favoured right-side, the Belgian took Tomovic out of the equation but scuffed his effort at goal.
Just as the game seemed to ebbing away from Fiorentina as the contest approached the hour-mark, Bernardeschi atoned for his earlier miss when his long-range effort took a wicked deflection off Ryan Mason and looped beyond Michel Vorm between the visiting sticks.
Matias Vecino, introduced for Tino Costa on 66 minutes, called Vorm into action with a rasping effort shortly afterwards.
Eric Dier’s introduction with twelve minutes to play signalled an admission from Spurs coach Mauricio Pochettino that a score draw is a positive result away from home.
Dele Alli went airborne to connect with Kieran Trippier’s delivery on 87 minutes but the Englishman’s acrobatic attempt flew over.
Gonzalo Rodriguez headed wide two minutes later as Spurs clung on.