Piatek was on fire in the first half, getting on the board in the 33rd minute and then doubling the score in the 36th, both off assists from forward Christian Kouame, reports Efe.
Frosinone forward Camillo Ciano successfully converted a penalty kick four minutes before first-half stoppage time, but his side could not come up with the equalizer in the second half.
Genoa climbed to seventh place in the Italian league standings with 12 points after four wins and two losses.
Frosinone, which was promoted to Serie A this season, is still in the second-to-last spot on the table with a single point.
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