Livorno almost took the lead shortly before Fiorentina scored when Ibrahima Mbaye was left unmarked, but headed off the crossbar.
The visitors went close again when Paulinho rounded Fiorentina goalkeeper Norberto Neto, but Gonzalo Rodriguez, who scored the only goal in the 66th minute, got back to clear off the line.
Fiorentina moved provisionally level on points with third-placed SSC Napoli, who were due to host UC Sampdoria yesterday. Livorno remained two points off safety.
Earlier, Cagliari missed a penalty as they were held to a 0-0 draw at lowly Chievo Verona.
Mauricio Pinilla blasted his spot-kick over the bar in the 66th minute after the Chilean forward had been tripped by Bostjan Cesar. It was the first penalty Chievo had conceded all season.
Both teams struggled to create any scoring opportunities. Chievo’s best chance came with their first sight of goal, just before the hour mark, when Cyril Thereau’s effort scraped past the outside of the post.
Cagliari extended their unbeaten run to seven, while Chievo snapped a run of two defeats and moved provisionally two points off the relegation zone.