Postecoglou is only two games away from clinching the J1 League Premiership and if the two time A-League Championship winning coach is to secure the title it would make him the first Australian manager to win Japanese football's biggest prize.
Yokohama's narrow win helped them leap-frog premiership title rivals FC Tokyo whose draw against Shonan Bellmare helped open the door for Postecoglou's side to go top for the first time this season.
While the finish line and championship success is in sight for Yokohama, Postecoglou was quick to temper any excitement among his squad instead extolling a simple message to the players.
"Just keep playing our football, that's what's got us to here," the former Brisbane Roar and Melbourne Victory boss said.
With more than 70 percent of possession, Marinos pressed for more goals but were denied by a dogged defensive performance from second-to-last Matsumoto, who face relegation after just one season back in the top flight.
"We knew it was going to be a difficult game, but we kept our discipline and the players were fantastic. They worked hard and we deserved the three points," said Postecoglou.
"It's not easy coming here. They put a lot of players behind the ball, even when they go 1-0 down, and we had to be patient."
Yokohama F.Marinos take on fourth placed Kawasaki Frontale next week before a final round grudge match against Tokyo FC which will most likely decide the title winner.
