Former Barcelona and Spain forward Villa, who moved from New York City FC ahead of the season in Japan, took advantage of some sloppy defending from Sagan Tosu to score the only goal in a 1-0 win.
Kobe, who also boast World Cup winners Andres Iniesta and Lukas Podolski in the side, came into the season as favourites but lost the first game of the season last week.
Sagan Tosu, who narrowly avoided relegation from the J.League last season, lost their first match of the season 4-0 and look set for another season of struggle.
Nagoya Grampus and Yokohama F. Marinos have started the season with two wins.
(Reporting by Jack Tarrant; editing by Sudipto Ganguly)
