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Guido Marilungo then nearly undid that bright start after intercepting Sorensen's short back-pass, but he could not find the target with a strike from close range.
As the match entered the final 15 minutes, Atalanta finally broke the deadlock as Davide Brivio's quick strike caught everyone by surprise, beating Curci to creep inside the far post.
Bologna were level just three minutes later, though, as substitute Rolando Bianchi made an immediate impact, nodding home the rebound after Jonathan Cristaldo's effort came crashing back off the crossbar.
Stefano Pioli's side were unable to hold out for a battling point as they conceded in a dramatic finale, with Curci culpable as Livaja's fierce drive went through his hands and into the net three minutes into stoppage time.