Nacer Chadli had put Spurs ahead with a dubious penalty before Federico Bernardeschi's deflected second-half effort sealed a closely-contested 1-1 stalemate - which leaves both sides fancying their chances in the return leg next week.
Dele Alli was again inspirational, especially in the opening half, but he was also lucky to avoid a red card for a kick aimed at a Fiorentina defender.
In the build-up to this tie, Mauricio Pochettino insisted he still had designs on winning the Europa League as well as competing for the FA Cup and Premier League back home.
But, in making seven changes from the weekend win over Manchester City which left them second in the table, the Spurs head coach was putting faith in his squad to deliver when called upon.
Ryan Mason captained the side on his first start since November, while Michel Vorm deputised for injured skipper Hugo Lloris in goal.
Tottenham had been knocked out here in Florence 12 months ago with another much-changed side - ahead of a Capital One Cup final against Chelsea just three days later.
It was a subdued start from both sides as neither goalkeeper was worked inside the opening 25 minutes until Christian Eriksen rasped a shot which Fiorentina's Ciprian Tatarusanu had to push behind for a corner.
Alli was booked for a petulant kick on Nenad Tomovic after he had already fouled the Viola defender on the touchline, with several Fiorentina players crowding referee Felix Zwayer.
The hosts should have taken the lead just after the half-hour mark as Josip Ilicic's cross fell to Bernardeschi six yards out, only for the winger to fluff his lines with Mauro Zarate stabbing the loose ball wide.
And they were made to pay for squandering a good chance as Spurs were awarded a penalty from their next attack as Ben Davies went down in the box after minimal contact from Tomovic.
Chadli, starting as the main striker with Harry Kane only amongst the substitutes, stood up and confidently stroked the resulting spot-kick past Tatarusanu.
Zarate wasted another decent chance as Jakub Blaszczykowski's cross was cleared into the path of the former West Ham United man, who fired over the bar just before the break.
Spurs thought they had doubled their advantage moments after the restart but Son Heung-min was offside as he dived to head in Eriksen's free-kick.
Mousa Dembele had been introduced by Pochettino at the interval and he set Chadli scampering away in search of a second, only for Tatarusanu to turn his angled effort behind.
But it was Fiorentina who would strike next as Bernardeschi let fly from long range, seeing his effort loop in over Vorm due to an unwitting deflection off Mason.
Pochettino turned to Kane with a little more than 20 minutes remaining as Son made way for the man who has already hit 19 goals for Spurs this season.
However, the England international could not add to that, with Fiorentina defender Gonzalo Rodriguez coming closest to producing a winner ahead of the return meeting at White Hart Lane.
Reigning Europa League champions Sevilla thrashed Molde 3-0 to almost certainly book their place in the last 16.
Fernando Llorente struck twice and Kevin Gameiro added a third as Ole Gunnar Solskjaer's men were blown away.
Villarreal will also defend a first-leg leg after beating Napoli 1-0 at El Madrigal.
Denis Suarez - who helped Sevilla win the Europa League last season - came up with the decisive moment when his dipping free-kick beat goalkeeper Jose Reina via the underside of the crossbar.
Goals from Lukasz Piszczek and Marco Reus handed Borussia Dortmund a 2-0 win over Porto.
Piszczek put Dortmund on the way to a comfortable victory after just six minutes at Signal Iduna Park and Reus made the result certain 19 minutes from time to leave Porto with an uphill task in Portugal next week.
St Etienne beat Basel 3-2 in an entertaining contest at the Stade Geoffroy-Guichard, with substitute Jean-Christophe Bahebeck the hero.
Moustapha Sall and Kevin Monnet-Paquet scored to put Les Verts in cruise control, but Basel were level by the hour mark through Walter Samuel and Marc Janko, the former Sydney FC star netting from the penalty spot.
But Bahebeck had the final word after 77 minutes to give St Etienne a narrow lead to take to Switzerland next week.
Anderlecht beat Olympiacos 1-0 at home with Kara Mbodji's controversial 67th-minute effort proving the difference.
The goal was only allowed after a lengthy discussion between referee and assistant referee, much to Olympiacos' displeasure who had complained of a foul on goalkeeper Roberto.
Athletic Bilbao won 1-0 at Marseille with Aritz Aduriz's spectacular 35-yard volley, his 26th goal of the season, splitting the sides.
Galatasaray and Lazio fought out a 1-1 draw - Sabri Sarioglu's early finish cancelled out by Sergej Milinkovic-Savic.
Shakhtar Donetsk and Schalke are also level after a goalless draw in Ukraine.
Bayer Leverkusen beat 10-man Sporting 1-0 away with Karim Bellarabi grabbing the all-important goal after 26 minutes.
Sporting will be without defender Ruben Semedo in next week's second leg in Germany after the defender was sent off for a second bookable offence after 74 minutes.
Fellow Portuguese side Braga had a better night with a 2-1 win against Sion in Switzerland, Nikola Stoiljkovic and Rafa Silva on target for the visitors with Moussa Konate replying.
Lukas Julis's second-half header gave Sparta Prague a slim 1-0 advantage over Krasnodar.