Genoa looked set to extend their strong recent home run after Andrea Bertolacci slotted home in the 72nd minute but Atalanta belied their own dismal recent away form by popping up with the equaliser to make it 1-1 four minutes into time added on.
It was well deserved for the visitors, who had the bulk of the chances in the match despite Genoa starting the stronger.
They had fired an early warning when Alberto Gilardino brought a decent save out of Andrea Consigli with a driven effort just two minutes in, and then in the 16th minute Luca Antonini's header went narrowly wide.
Atalanta heeded the warning and shifted play to the other end, where Stefano Lucchini went close with a header before German Denis brought a decent save out of Mattia Perin with a low shot.
As half-time neared, Cigarini curled a shot narrowly wide.
Atalanta remained on top as the second half started, but Maxi Moralez and Lucchini blazed over in quick succession.
Yet it was Genoa who took the lead through Bertalacci with a smart finish at the far post with 72 minutes gone, and Atalanta looked destined for a ninth defeat in 10 on the road this season after De Luca sent a shot high over the bar.
But just when it seemed to be all over, Cigarini crossed from the right and De Luca was presented with a tap-in.