Destro seals victory for Roma
The win moved Roma back within three points of Italian league leader Juventus, which beat Bologna 2-0 Friday.
Right back Maicon put Roma ahead from close range seven minutes in at the Stadio Olimpico after being set up by Gervinho.
Juan Vargas equalized for Fiorentina in the 29th with a powerful shot after Nenad Tomovic carried the ball deep into the area.
Destro's winner came in the 68th after he also was set up by Gervinho in the area.
Among Europe's major leagues, only Roma and Bayern Munich remain unbeaten.
Roma visits Juventus in January immediately after the winter break.
Destro, a forward who has also played for Italy, had his left knee operated on in January and played sporadically at the end of last season then took more time off after experiencing further pain and swelling.
Two minutes after Destro's goal, Roma goalkeeper Morgan De Sanctis preserved the lead by leaping to tip away a dangerous free kick from Fiorentina captain Manuel Pasqual in the 70th.
Roma midfielder Kevin Strootman had hit the post in the 62nd.
Roma played the final two minutes with 10 men after Miralem Pjanic picked up his second yellow card.
Roma opened the season with a record 10 wins but had struggled in recent matches without its 37-year-old captain Francesco Totti, who was on the bench for the first time Sunday after being out since October with an injured right hamstring.
Fiorentina remained level fifth with Inter Milan, which hosts Parma later.