Fiorentina have the second-best home record in Serie A this season, but they sat back and let Spurs dominate possession throughout the first half, with Christian Eriksen and Dele Alli pulling the strings for the visitors.
© Getty Images
However, Spurs struggled to create many clear-cut chances and the first quarter of the game went by without either goalkeeper being worked.
Eriksen warmed the palms of Ciprian Tatarusanu with a strike from distance in the 26th minute, but Spurs were then lucky not to be reduced to ten men when Alli kicked out at Nenad Tomovic off the pitch. German referee Felix Zwayer appeared to see the incident, but only booked the teenage midfielder.
Moments later Fiorentina spurned a superb chance to take the lead when Federico Bernardeschi miskicked from just five yards at the back post. The ball dropped to Mauro Zarate, but he could not wrap his foot around it under pressure.
Spurs' first-half dominance eventually told in the 37th minute when Tomovic went to ground and tripped Ben Davies in the area. Zwayer immediately pointed to the spot and with no Harry Kane in the starting lineup, stand-in striker Nacer Chadli stepped up and slotted home from 12 yards.
Zarate shot over with a half-chance just before the break, but Spurs were soon on top again upon the resumption as Son Heung-Min had a goal disallowed for offside before Chadli saw a shot tipped wide by Tatarusanu.
Spurs looked so comfortable, but that all changed in the 59th minute when a speculative 30-yard shot from Bernardeschi looped up off Ryan Mason's boot, over Michel Vorm and into the net off the underside of the crossbar.
The goal gave Fiorentina and their supporters a big lift and they were the side doing more of the pressing in the final half-hour.
Spurs brought on top-scorer Kane, but he struggled to make an impact, with Alli's audacious overhead effort that flew over the closest they came to going back in front.
Down the other end, Fiorentina centre-back Gonzalo Rodriguez headed wide from close range with a golden late chance to win it, so the match finished all square ahead of next week's return leg at White Hart Lane.