Antonio Floro Flores gave the Grifone an early lead, but Cristiano Del Grosso replied within two minutes to earn the Nerazzurri a point and maintain a nine-point gap over their rivals with five games of the season remaining.
Visiting coach Stefano Colantuono was sent off in a fiercely-contested encounter.
Genoa were back at the Stadio Luigi Ferraris, but this time as the home team after a draw at city rivals Sampdoria a week ago.
That result left them on the wrong side of the drop zone and needing to react against Atalanta, which they did immediately, taking the lead in the sixth minute.
Floro Flores rose to beat Del Grosso in the air and head past Andre Consigli.
The joy was short-lived for the Rossoblu, though, with Del Grosso making up for his mistake by bringing Atalanta level.
Former Sampdoria defender Stefano Lucchini's header was pushed behind by Sebastien Frey, but he could do nothing to prevent an unmarked Del Grosso shoot past him from the edge of the area from the resulting corner.
Neither side held back and the referee had a job on his hands keeping a lid on a game which looked like it would explode at any time.
Genoa went close to making an equally impressive start to the second half when Bosko Jankovic's shot only just missed the target.
The tension on the field spilled over onto the bench in the 57th minute and Colantuono was sent off by the referee, who took exception to his vehement protests.
The game continued to be a scrappy affair with Genoa desperate to get all three points, but equally desperate to keep their opponents from taking the lead.
However, apart from a few shots from long distance, Genoa never threatened a winner as they failed to move out of the bottom three.
The gap to safety could grow to four points on Sunday should Siena beat Chievo.