Bankrupt and well adrift at the bottom of Serie A for many months, Parma somehow found the pluck to secure a draw at Inter Milan before beating Udinese and then champions-elect Juventus to inspire a glimmer of hope.
But notching a third straight win was a bridge too far and goals in either half from Iago Falque and Leonardo Pavoletti at the Marassi condemned Parma to their 21st defeat of the season.
Genoa rose to seventh in the table on the back of a second consecutive victory, and a Europa League place is now only six points away.
Falque flashed Parma an early warning by nutmegging Zouhair Feddal to create a one-on-one with Antonio Mirante, from which he shot well wide.
His aim was true in the 14th minute, however.
Striker Marco Borriello won back possession in the Parma half before supplying Falque, who fired an unstoppable left-footed drive past the stranded Mirante.
Genoa kept pushing forward and Alassane Tambe was only denied the second goal by quick thinking from Feddal as he looked to head home Diego Perotti’s cross to the far post.
Then, just after the half-hour mark, Falque freed up Pavoletti for another one-on-one. This time the effort was much worse than the Spaniard’s first and Parma somehow reached the break only one goal down.
Mirante flew across his goalmouth to deny Perotti a splendid strike shortly after play resumed.
In a rare Parma break Mattia Cassani supplied a clever cross that Abdelkader Ghezzal reached but stuck wide under pressure from Tambe.
Falque was unlucky not to hit the target with a wicked free-kick in the 72nd minute and only a reaction save from Mirante kept Juraj Kucka out when the Slovakian burst into the box moments later.
With Parma on the ropes, the Grifoni made it 2-0 in the 76th minute.
Perotti’s assist for Pavoletti was an intelligent one and the on-loan Sassuolo striker controlled the ball with one boot before tricking Mirante with the other.