The Sydney fixture was forced into extra-time when the sides ended 90 minutes tied at 1-1 and, after the additional half-hour failed to produce another goal, Keisuke Honda and Shinji Kagawa missed their respective spot-kicks to cost Japan a place in the last four.
After Kagawa's effort had struck the left-hand post, Ismail Ahmed stepped up to seal the win for UAE.
Javier Aguirre's side stepped up their game somewhat in the second half, and pulled level through Gaku Shibasaki nine minutes from time.
The victory sees Mahdi Ali's side progress to face hosts Australia for a place in the final, while Japan suffer their earliest elimination since 1996, when the tournament was held in UAE.
That tournament was also the last time UAE - eventual runners-up - reached the last four.
The 24-year-old expertly brought down an inviting ball over the top, before rifling his fourth goal of the tournament across Eiji Kawashima into the bottom-left corner.
Inui looked to be Japan's biggest threat early on and should have netted a leveller 11 minutes later, but headed straight at Majed Naser from a Gotoku Sakai cross.
With the winners of the fixture going on to face hosts Australia in the semi-finals, it was little surprise to hear the lower-ranked UAE enthusiastically supported in Sydney, and Ali's men looked assured in preserving their unexpected lead.
Yoshinori Muto was introduced in place of Inui at the interval, but squandered two great opportunites to pull Japan level - drilling wide left before sending a header off target just short of the hour mark.
There was no questioning Japan's improved attacking threat in the second half, and their persistance paid off when Shibasaki produced a sublime finish nine minutes from time.
The substitute was teed up by Honda just outside the box and found the net with a perfectly judged curling strike.
Only some desperate defending prevented Japan snatching the win in normal time, with Naser punching clear from a Kagawa effort late on before pushing over from a Honda free-kick.
Kagawa then put the ball agonisingly wide of the left-hand post from close range with the final kick of regulation time to force an extra 30 minutes.
The first period of additional time passed without incident - much to the relief of UAE, who came under immense pressure towards the end of the 90 - and the pace barely picked up in the second, with a late Honda free-kick sneaking just wide of the target to leave the sides to contest a shootout.
Kagawa's strike against the base of the post at 4-4 opened the door for Ahmed to seal a famous victory, and the substitute made no mistake from 12 yards.
