Roma coach Rudi Garcia was delighted after his side moved to only one point from leaders Juventus.
With the Bianconeri only managing a draw at home against Sampdoria, Roma were determined to get all three points from the Genoa game and Radja Nainggolan's acrobatic volley was enough to move closer to the top of the Serie A table.
"The lads did a good job, they took full advantage [of Juventus' draw] to move -1 in the table," Garcia said.
"Winning here [in Genoa] is a great result, we had chances in the second half, it would have been useful to score the second to avoid suffering in the end.
"The disallowed goal [Tomas Rincon's goal] was a good decision to disallow, I would instead say that it was strange that the corner was given.
"[Radja Nainggolan] is one of the best in the league but I expect him to always perform like this as he's involved in both the offensive and defensive moves."
Roma host Milan next week before the Christmas break and the Frenchman wants all three points before the holidays.
"A win against Milan would be the perfect [Christmas] gift to the fans, the club and the president," added Garcia.