Bryan Cristante scored in the 75th minute with a shot from the edge of the penalty area to leave the top-flight debutants firmly rooted to the bottom of the table.
Benevento's start is the worst ever in the top five European leagues including England, Spain, Germany and France.
The previous record of 12 defeats at the start of the season was set by Manchester United in 1930-31.
Atalanta are 10th with 19 points.
(Reporting by Brian Homewood; Editing by Ken Ferris)
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