Christian Tello - on loan from Barcelona, but not named in Fiorentina's Europa League squad - and Nikola Kalinic scored after 81 and 87 minutes respectively to secure a 3-2 win at Atalanta.
That stretched La Viola's run to six unbeaten in Serie A as they held onto third place.
Since the turn of the year, Fiorentina have scored in the final 10 minutes of six of their 10 games in all competitions.
Meanwhile, Braga are the first team through to the last 16 after a 2-2 draw at home to Sion on Wednesday night completed a 4-3 aggregate win.
Here how it stands in the Round of 32...
EUROPE LEAGUE - SCORES AFTER R32 FIRST LEG
SPURS 1-1 FIORENTINA
Fenerbache 2-0 Locomotiv Moscow
Anderlecht 1-0 Olympiacos
Midtjylland 2-1 Manchester United
Borussia Dortmund 2-0 Porto
Villareal 1-0 Napoli
St Etienne 3-2 Basel
Sevilla 3-0 Molde
Sporting CP 0-1 Bayer Leverkusen
Valencia 6-0 Rapid Vienna
Augsburg 0-0 Liverpool
Sparta Prague 1-0 Krasnodar
Galatasaray 1-1 Lazio
Shakhtar Donetsk 0-0 Schalke
Marseille 0-1 Athletic Bilbao
SECOND LEG RESULT
Braga 2-2 Sion - Braga win 4-3 on aggregate