Rodrigo Palacio put the visitors in front in the seventh minute but the rest of the game belonged to Novara, who had to wait until the 68th minute to finally grab an equalizer through Giuseppe Mascara.
Genoa's rearguard proved impossible to breach for a second time and Novara striker Andrea Caracciolo was shown a late red card for a foul borne of frustration.
Alberto Malesani took his place on the Genoa bench after being re-hired to replace axed coach Pasquale Marino, and he was soon on his feet celebrating the opening goal.
Palacio was credited with it, although his shot took a final touch off Marco Rossi as it found the net to stun the home side.
Their response came from former Sampdoria striker Caracciolo, whose shot was saved well by Sebastien Frey.
Caracciolo continued to create problems for the Genoa defence, who were far busier than their Novara counterparts as the home side pushed for an equaliser.
Mascara was sent on by Attilio Tesser as a third striker, and the gamble paid off with the former Catania man scoring just 10 minutes after taking to the field.
Frey punched the ball away from a left-wing cross and Mascara picked up the ball outside the penalty area, and his shot came back through a crowd of defenders with the Genoa goalkeeper seemingly unsighted as it flew into the bottom corner.
In the 71st minute, Palacio's volley grazed the outside of the post, but it was only a rare attack from the Rossoblu as Novara continued to press.
Caracciolo spurned another opportunity in the penalty area as Novara maintained a steady assault on the Genoa goal.
The Novara striker let his frustration get the better of him in the last minute, though, when he was shown a straight red card for a dangerous tackle on Davide Biondini, leaving the Piedmontese side to defend a point, successfully, over the five minutes of stoppage time.