Many were brought to tears, including Juventus captain Gianluigi Buffon, as a minute's silence was held at the top-flight grounds.
After the win, Fiorentina sit in the ninth spot in the Serie A table with 38 points, while Benevento remain in the last place with only ten points.
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Both sets of supporters stayed nearly completely silent for five minutes in a respectful and moving tribute to Astori, with Fiorentina coach Stefano Pioli struggling to hold back his emotions as the overwhelming occasion saw him shed a tear on the incredibly hard day.
Astori died in his sleep aged just 31.
Earlier this Fiorentina announced they would be retiring the shirt in memory of their former captain.
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The only goal of the game was scored by Vitor Hugo, the man who replaced Astori in defence and who wore the Number 31 jersey - the reverse of Astori's 13.
Fiorentina could have added a second in stoppage time at the end of the second half as Milan Badelj hammered a shot from distance off the post, and Marco Benassi somehow blazed the rebound over the bar.
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