Samurai Blue have reached the last-16 stage of a World Cup on three previous occasions, and they have placed themselves in a strong position to advance to the first knockout round of the 2022 competition.
Japan fell behind in their Group E opener against Germany on Wednesday, with Manchester City midfielder Ilkay Gundogan finding the back of the net from the penalty spot.
However, two substitutes turned the match around for Moriyasu's side, with Ritsu Doan levelling the scores in the 75th minute before Takuma Asano struck the winner eight minutes later.
Japan are next in action against Costa Rica on Sunday, and a victory would send them through to the last-16 stage of the competition if Germany fail to overcome Spain in the later match in the section.
Moriyasu has said that his team want to 'build their own style by learning from other countries', with eight of their current squad playing their club football in Germany.
"Japan wants to build its own style by also learning from other countries," coach Moriyasu told reporters during his pre-match press conference.
"We have eight players in the German leagues, we are grateful to German football for their cooperation. Their coaches and our players (playing in Germany) have been helping us to grow and we continue learning from them."
Meanwhile, Japan captain Maya Yoshida said that the "spotlight" is on his side following their victory over Germany, and the experienced centre-back has called for "calm".
"Make no mistake, when you win you feel more comfortable," said Yoshida. "We have to stay calm, prepare well and concentrate on the plan to get us the win.
"The spotlight is on us after the last game and we have to make sure that we don't dance badly. We're not through yet."
Japan have never lost an international game to Costa Rica, winning four of their previous five meetings, which have all been friendlies, including a 3-0 victory in their last clash in September 2018.