Pointless Poland and Colombia meet later Sunday in Kazan with the last-16 spots determined next Thursday.
The draw means both nations go into the final round of matches on four points at the top of the group.
A poor headed clearance landed right at Youssouf Sabaly's feet and although goalkeeper Eiji Kawashima managed to parry the defender's stinging shot from the left, the ball rebounded into the net off Mane's knee.
Mbaye Niang should have restored Senegal's lead five minutes before the break when he broke through on goal, but failed to beat the keeper in a one-on-one as the half ended 1-1.
Backed by a vocal Japanese following who never stopped singing and with the locals also on their side, Japan were now the better side after a nervous start. Honda came on the field a minute later and evened the score.
Working down the Africans' left side, the 26-year-old talisman Mane was only a sporadic danger.
And it was Senegal who retook the lead five minutes later as Wague met a ball played across the box and coolly sidefooted into the roof of the net for his first global goal.
Against the run of play Moussa Wague put Senegal ahead on 71 minutes but Japan fought back again and Keisuke Honda salvaged a point 12 minutes from time.