The match, postponed in early November because of flooding in Genoa, also marked the return of Inter forward Diego Forlan who was injured after scoring in Uruguay's World Cup qualifier in Paraguay in October.
Forlan looked lively after he came on for Diego Milito in the 82nd minute, ending another frustrating, scoreless night for the Argentine.
Inter, 15th before last weekend's matches, moved level on 20 points with sixth-placed Palermo after 14 games. Genoa, who have fallen away after a promising start, are two points behind.
Genoa goalkeeper Sebastien Frey kept his team on level terms in the first half, denying Giampaolo Pazzini early in the game and then making a superb double save from Walter Samuel's header and Milito's effort from the rebound.
Genoa thought they had gone ahead after half-time when Andreas Granqvist headed in but his effort was controversially disallowed for offside.
Inter broke through in the 67th minute when Ricky Alvarez's inviting inswinging cross was headed home by the unmarked Nagatomo.
The Japanese player also had a key role at the other end, heading away Marco Rossi's goalbound shot late in the game.
Inter goalkeeper Julio Cesar then saw some rare action as he turned Miguel Veloso's curling effort over the bar.
