Gaetano D'Agostino gave Pescara the lead in the 24th minute and for a time it looked like the change in coach would have the desired effect, but German Denis levelled from the penalty spot within 10 minutes.
Denis' second early in the second half finished off Pescara and earned the Bergamese side all three points, moving them up to mid-table.
Bucchi took his place on the Pescara bench for the first time following the dismissal of Christian Bergodi last weekend, and he appeared to have worked on the basics in his first few days in charge.
Pescara, captained by Giuseppe Sculli for the first time, looked particularly organised in defence and keen to get men forward on the counter-attack, with Vladimir Weiss and Ante Vukusic providing width.
The visitors took the lead in the 24th minute with D'Agostino firing a shot into the top corner of the goal from the edge of the area.
The Delfini's lead lasted just 10 minutes before a challenge by Zanon on Giacomo Bonaventura was punished by the referee, who awarded a penalty.
Denis stepped up to the spot and sent Ivan Pelizzoli the wrong way to bring the home team level.
Atalanta were back in the game and soon threatened again with a dangerous cross from Cristiano Del Grosso just too far in front of Marko Livaja.
The Nerazzurri took the lead in the 67th minute, with Davide Biondini's cross taken down well by Denis on his chest before he struck the ball powerfully into the roof of the net from close range.
Giuseppe De Luca went close to making it three in the 80th minute, but Pescara did not hoist the white flag.
Sculli almost picked out Vukusic in the centre, but Stefano Lucchini got to the ball first to deny him a free header from close range.
Vukusic shot wide from just outside the penalty area as Pescara kept pushing to the very end, without managing to find a way through.