Head coach Mauricio Pochettino made six changes for the first leg of the last 32 clash as Tottenham tackled the first of six games in 17 days across three competitions, but his remodelled line-up dominated the opening exchanges after recalled forward Roberto Soldado scored a fine sixth-minute opener.
But Soldado was partly culpable for the Fiorentina equaliser, bringing down Joaquin before the subsequent free-kick fell kindly for Jose Basanta to score a vital away goal.
Nacer Chadli struck the crossbar late in the first half for Tottenham, but their Serie A opponents matched them throughout the second period.
Vincenzo Montella's Fiorentina were good value for extending their unbeaten to nine matches as the Premier League team's earlier rhythm eluded them.
Soldado slipped a clever pass through the Fiorentina defence for Chadli to draw a sharp save from Ciprian Tatarusanu and the Spain international fired his team ahead in style from the resulting corner.
Paulinho's outswinging delivery found Soldado in ample room 15 yards from goal and the striker swivelled to rifle home an excellent volley.
On-loan Chelsea winger Mohamed Salah had an attempt blocked by Jan Vertonghen on a rare moment of encouragement amid a torrid opening half hour for Fiorentina.
Tottenham playmaker Christian Eriksen lifted over from 18 yards before Soldado sent an overhead kick into Tatarusanu's arms.
The hosts found repeated joy down the right flank, with Andros Townsend cutting in to see a shot deflect wide in the 31st minute, but Basanta put his troubles on the left of Fiorentina's back three to one side when he equalised nine minutes before half-time.
Matias Fernandez whipped a vicious free-kick towards the near post, Hugo Lloris' punch struck Fiorentina defender Stefan Savic on the back and dropped to leave Basanta with a simple finish.
Pochettino's team almost restored their lead on the stroke of half-time when Tatarusanu kept out a Soldado header from Kyle Walker's cross and Chadli turned the rebound against the underside of the crossbar.
Salah whipped an effort narrowly wide from the edge of the box as Fiorentina began the second period in far more encouraging fashion.
In the 56th minute, Eriksen found himself crowded out by a visiting defence showing far greater composure and restricting Tottenham to half chances.
It persuaded Pochettino to send top scorer Harry Kane on for Chadli midway through the half, but the home team were almost exposed at the back as Mario Gomez cut in past Federico Fazio to blast over.
Paulinho's influence had waned since the early action, but the Tottenham midfielder made a well-timed run into the box in the 72nd minute, only for Tatarusanu to save once more.
Fiorentina came closest to snatching the win as time ticked down - the impressive Joaquin slipping a pass to substitute Marcos Alonso, whose cross from the left channel flashed agonisingly past Gomez's outstretched boot - but Montella will be the more content coach ahead of next week's return.
