The Greece international scored the only goal of the game to help his side to the full three points against the Serie A runners-up
The Giallorossi had a number of chances to open the scoring but were made to pay for their profligacy in front of goal by Giannis Fetfatzidis' winner.
The first serious chance of the game fell to the away side after 10 minutes of play. Radja Nainggolan tried his luck from the edge of the area after Genoa failed to clear a corner kick, but the Belgium international failed to to get his shot on target.
Genoa first threatened halfway through the first half when Giovanni Marchese met a Giuseppe Sculli cross, but the defender's header was kept out by Lukasz Skorupski.
The Romans continued to dominate and once more looked dangerous when Mattia Destro set up Adem Ljajic, but the Serbian attacker failed to beat Mattia Perin and the chance went begging.
Rudi Garcia's men kept on pushing for the opener after the interval and again Nainggolan attempted to test the Genoa shot stopper after some nice work from Ljajic down the right, but his shot was deflected wide for a corner kick.
Genoa then went 1-0 up in the closing stages of the game against the run of play when Fetfatzidis found the with a calm finish after some poor defending from Nainggolan.
Roma finish the 2013-14 campaign in second place with 85 points from 38 games to qualify for next season's Champions League.
Genoa, meanwhile, end the season in joint 13th position with 44 points.