Two quick-fire first-half goals from Giuseppe De Luca and Marcelo Estigarribia earned Stefano Colantuono's men all three points to take them to within two points of the top five and keep their hopes alive of qualifying for Europe next season.
Bologna, meanwhile, could slip into the bottom three on Sunday with rumours growing that Stefano Pioli will be back on their bench for the trip to Inter Milan next weekend.
The pressure was growing on Ballardini with his side having won only two of their past 13 games, and after a tight opening 20 minutes, they fell behind to De Luca's goal.
German Denis made room with a decoy run opening up space for him to exploit, and his left-foot shot from just inside the area was unstoppable for Gianluca Curci.
Bologna's shock turned to stunned silence four minutes later when an efficient Atalanta doubled their advantage.
De Luca set up Estigarribia, who did not appear to have too much on when he opted to shoot with the ball sailing into the top left-hand corner from nearly 30 yards.
Atalanta goalkeeper Andrea Consigli was happy to deny Jose Crespo an immediate equaliser having only fumbled an effort from Lazaros Christodoulopoulos to the feet of the Bologna full-back, and he did well to deny the Greek midfielder again five minutes later.
Davide Moscardelli wasted a chance to bring Bologna back into the game as he headed too close to Consigli before another fine save from Consigli on Acquafresca ensured Bologna took a somewhat fortunate two-goal lead into the interval.
Consigli was soon in the thick of the action in the second half too, denying Jonathan Cristaldo, although he was lucky in the 76th minute that Guglielmo Stendardo put the ball behind after Moscardelli's shot hit his shoulder.
It proved to be the last time the Atalanta goal was tested as Bologna lost their belief and the game, remaining just two points above the relegation zone ahead of Sunday's Serie A fixtures.