Quagliarella, who turns 36 next week, matched the mark after converting a penalty after 31 minutes against Udinese.
Batistuta scored at least one goal per game in the opening 11 games of the season in 1994-1995 for Fiorentina. The Argentine went on to finish the season as the top scorer with 26 goals.
Quagliarella has had one of the best seasons of his career with Sampdoria. He has scored 13 goals in his 11-match run for a total of 15 this season.
The 25-times capped Italian international scored a career best 19 goals last season.
He joined the Genoa club in 2016 having previously played for teams including Juventus, Napoli and Torino.
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