Japan, whose women's side have already progressed to their gold-medal match, sneaked ahead after an evenly-contested beginning to the encounter.
Their lead came in some style too, as Otsu struck a superb half-volley into the top corner after collecting the ball from Keigo Higashi on the edge of the box.
Mexico responded positively to falling behind, with Tottenham Hotspur's forgotten man Giovani dos Santos the focal point of their attack.
The Spurs winger went close to levelling the match as he bent a shot inches wide of the post.
Mexico did net an equaliser from their next attack as Fabian met a Dos Santos corner at the near post with a powerful header.
Dos Santos could have sent his nation into the break ahead, but his chipped effort went narrowly over the crossbar to leave the match even at half-time.