Fourth-placed Juventus's 3-1 win at Sampdoria on Saturday put the pressure on Atalanta to keep pace in the race for the Champions League qualification spots, and a home game against 19th-placed Genoa seemed a gift.
However, other than Luis Muriel's first-half effort that clipped the outside of the post, Atalanta struggled to break down a determined Genoa.
The visitors started to create chances of their own with fresh legs off the bench, with Mattia Destro drilling just wide, but they could not find a winner and settled for a deserved point.
While Atalanta have played one game fewer than Juventus, the fact that they have achieved just one win in seven Serie A matches has left them with a mountain to climb to secure Champions League football for next season.
Genoa remain six points from safety after a seventh successive Serie A draw.