Pescara, who fired Cristiano Bergodi after taking only one point from their previous eight games, went in front in the 24th minute when Gaetano D'Agostino rifled the ball in from the edge of the penalty area.
Their lead lasted only 10 minutes before mid-table Atalanta were awarded a penalty for a foul on Giacomo Bonaventura and Argentine striker German Denis converted.
Former Napoli and Udinese forward Denis struck again in the 67th minute when Davide Bondoni's cross found him unmarked by the Pescara defence, leaving him with enough time to chest the ball down and score his 11th goal of the league season.
Pescara, who have both the worst attacking and defensive records in the league, are level on 21 points at the bottom with Palermo and Siena, who were meeting later on Sunday.
Bucchi, a much-travelled forward in his playing days, was promoted from the role of youth team coach following Bergodi's dismissal.