Roberto Soldado had volleyed home Paulinho’s corner after just six minutes but the striker conceded the free-kick from which Jose Maria Basanta levelled 10 minutes before the break to leave the game finely-poised ahead of next week’s second leg.
Former Chelsea winger Mohamed Salah spurned a number of opportunites to grab a second away goal for his side, while Harry Kane was brought on for the final quarter of the game, in which both sides failed to create anything clear cut.
Spurs, whoface a gruelling run of six fixtures in 17 days, travel to Florence just three days before the Capital One Cup final hoping to reach the last 16 for the second successive season, but they will have a difficult task on their hands against a side that has lost just one in their last 12 games in Serie A.
Mauricio Pochettino made six changes to the side which lost 3-2 at Liverpool and they seemed to have the desired effect as Spurs flew out of the blocks.
Nacer Chadli, who made his first start in seven matches, was played through on goal by Soldado and drew a fine save from Tatarusanu.
But Spurs were not to be denied as Soldado volleyed Paulinho’s resulting corner across goal into the unguarded net.
Fiorentina had a couple of half-chances to draw level against the run of play but Mohamed Salah, who returned to London for the first time since his move to Italy, and then Joaquin failed to find the target.
Mario Gomez had strong claims for a penalty when Jan Vertonghen appeared to catch the former Germany international in the box, but referee Carlos Velasco Carballo was unmoved.
Andros Townsend gave his opposite number, left-back Basanta, a torrid time for large parts of the first half but failed to take advantage of his, and his side’s, dominance as the Argentine levelled the tie before the break.
Soldado came within inches of giving away a penalty as he chopped down Joaquin close to the box but Fiorentina did draw level as Fernandez’s drilled free-kick was parried by Hugo Lloris into the path of Basanta, who rifled home from six yards.
The Viola grew in confidence but it was Spurs who had the best chance before the break as Chadli scooped Soldado’s saved effort back towards the unguarded goal.
Having beaten the goalkeeper, the ball cannoned off the crossbar and down on the goal line, but the officials judged it to have not crossed the line.
The visitors started the second half the better of the two sides as Salah found space at the edge of the box but was unable to find the back of the net with a left-footed strike.
Spurs weathered an early second-half onslaught from the Italians but failed to convert the first chance of the half as Christian Eriksen and Soldado overplayed the ball when breaking after David Pizarro was dispossessed.
Kane’s inclusion with 25 minutes remaining did little as Spurs struggled to snatch the advantage ahead of next week’s trip to Italy.
And, as the game grew on, the visitors looked the likelier to find the back of the net as Salah failed to make the most of several sights of goal in the closing stages.