Ryan Mason gave Spurs the lead with a composed finish in the first half and Erik Lamela made it two before a Gonzalo Rodriguez own goal completed a 4-1 victory on aggregate.
The only blemish on another excellent night for Mauricio Pochettino's men saw Dele Alli pick up his third yellow card of the competition, which means the 19-year-old is banned for the first leg of the next round.
Kane was left out of a Spurs matchday squad for the first time this season as he recovers from a broken nose but Pochettino showed the seriousness with which he continues to treat this most exhausting of competitions by fielding all of his other key players including Hugo Lloris, Eric Dier and Alli.
The cost of his commitment may be better gauged on Sunday, when his side resume their title charge at home to Swansea, or even later next month, with the two quarter-final legs coming in the middle of a six-week period that includes league matches against West Ham, Arsenal, Liverpool and Manchester United.
One blessing at least may be that the opponents immediately following the two European ties will be the less daunting Aston Villa and Bournemouth.
For now though, this was an important victory, not least to recover momentum following last weekend's shock FA Cup exit at the hands of Crystal Palace, a defeat which brought to an end Tottenham's eight-match unbeaten run and set nerves jangling amongst the Spurs faithful.
Mason's goal was also timely, for him after an injury-interrupted campaign, and for Pochettino, who will hope it can spark a return of confidence and form for the midfielder, whose role could become significant while Mousa Dembele remains absent with a groin strain.
Spurs had a strong case for a penalty in the opening 10 minutes when Marcos Alonso seemed to block Kieran Trippier's cross with his hands and then Dier flicked Lamela's cross to the back post but it was too far ahead of the lunging Alli.
With 25 minutes on the clock, the hosts did break the deadlock as Alli beat the diving Davide Astori to Ben Davies' ball forward and his slight touch was enough to set Mason free, as the midfielder burst through before applying a cool finish into the far corner.
Nacer Chadli, quiet in the first half as Kane's stand-in up front, thought he had doubled Tottenham's lead at the start of the second when he finished off Lamela's through ball but the Belgian had strayed offside by a whisker.
Fiorentina, just as they did in the first leg, grew in confidence as the game approached the hour but they lacked cutting edge, succinctly demonstrated by Federico Bernardeschi - the talented number 10 reportedly catching the eye of various top European clubs - comically slicing his shot out for a throw-in.
Spurs were more clinical and in the 63rd minute they doubled their lead as Christian Eriksen's reverse pass set Chadli clear and while his shot was saved, Lamela showed a cool head to steer home the follow-up for his sixth goal in six Europa League games this season.
Tottenham had the game all but sewn up but there was one stain on an otherwise perfect evening as Alli was booked for falling to the ground too easily, his third yellow card in the competition meaning he will be suspended for the first leg of the last 16.
Groans turned to cheers moments later, however, as another excellent Trippier cross was turned in by Fiorentina's Rodriguez to cap another resounding victory in North London.
Source : PA
Source: PA