The Bergamo-based club rose above Roma into fifth place in Italy's top tier. Thanks to the performance of Italian clubs in Europe, the top five will qualify automatically for the Champions League.
Atalanta rested some regular starters with one eye on Thursday's second leg of the Europe League semi-final against Marseille
They went behind after 18 minutes when Loum Tchaouna scored against the run of play.
But Atalanta woke up in the second half. Gianluca Scamacca converted a nice headed assist by Mario Pasalic, and six minutes later Teun Koopmeiners stroked home from outside the box.
Salernitana remain on the bottom of the table and will spend next season in Serie B.
In the day's other match, Udinese equalised deep in stoppage time to draw with Napoli 1-1 at home and earn a vital point in their fight against relegation.
Substitute Isaac Success was surrounded by defenders but managed to squeeze a shot home in the second minute of stoppage time.
Until then, it had looked like a certain defeat for the home side after Victor Osimhen scored his 15th league goal five minutes into the second half.
Osimhen rose to power home an inviting cross from Matteo Politano. The Nigeria international also had a goal chalked off 10 minutes from the end.
Udinese remained third from the bottom and in the relegation zone, two points behind Empoli and Frosinone.
Three rounds remain and six teams are fighting to avoid joining Salernitana in the second division.
Napoli are eighth, one point ahead of Fiorentina.
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