After being pushed all the way in their opening Group F victory over Turkmenistan, Japan were again far from their best as two contentious penalty decisions proved pivotal on Sunday.
Genki Haraguchi scored the only goal after Raed Saleh was adjudged to have fouled him just before the half hour, while Yuto Nagatomo was lucky not to concede a spot-kick at the other end for handball.
Victory means Japan progress to the knockout stages, while Oman could join them as one of the best third-placed teams should Uzbekistan beat Turkmenistan and they do the same on Thursday.
After Faiyz Al Rusheidi impressed early on with a number of smart saves, Oman almost took the lead after 20 minutes when Muhsen Al Ghassani rounded Shuichi Gonda, but his effort from a tight angle rolled wide of the post.
Al Rusheidi made another stop to deny Takumi Minamino in the 27th minute but Japan were soon ahead as Saleh conceded a penalty for fouling Haraguchi, although replays suggested there was little contact.
Haraguchi scored from the spot but Japan were lucky to go into the break level after defender Nagatomo appeared to block Salaah Al-Yahyaei's late shot with his hands.
Adding to their lead proved tough for Japan after the break and the Samurai Blue were grateful to poor Oman decisions in the final third as they clung on to victory.