A Josip Ilicic free-kick and late Rafal Wolski strike were enough to see off the challenge of Atalanta, who ended the game with 10 men after losing Luca Cigarini to a red card nine minutes from time.
The win puts the pressure on Napoli, who host AC Milan on Saturday night now level on points with the Viola as the battle for places in the Champions League next season intensifies.
Fiorentina had two reasons to be angry as they hosted Atalanta, keen to bounce back from defeats in Serie A and the Coppa Italia over the past week.
They nearly took the lead against Atalanta in the 10th minute when Juan Cuadrado nearly got his ball through to Juan Vargas, but Cristian Raimondi cleared the danger.
The Viola took the lead six minutes later when Ilicic curled in a left-footed free-kick inside the near post, beating Andrea Consigli's attempts to keep the ball out.
Anderson, making his starting debut for Fiorentina following his move from Manchester United, then tested Consigli as the home team looked to build on their lead.
Atalanta's calls for a penalty were waved away after half an hour when Maxi Moralez went down under the challenge of Fiorentina goalkeeper Neto, who then did well to stop Giacomo Bonaventura's shot from the edge of the area.
Atalanta, who put three past Napoli a week ago, were starting to get into the game and Bonaventura was again denied by Neto, who subsequently cut out a dangerous cross from Moralez.
Borja Valero nearly made it two 10 minutes into the second half, but Consigli dived to make the save and keep Atalanta in the game.
The Viola upped their search for a second goal and the lively Wolski caused plenty of problems following his introduction.
Atalanta's hopes of finding a leveller were dealt a blow when Cigarini picked up a second yellow card in the 81st minute, and Fiorentina took advantage of the extra man to seal victory through Wolski, who beat Consigli with a right-footed effort in the 86th minute.