Shinji Kagawa had missed the first sudden-death penalty leaving Ismail Ahmed to nervelessly convert the decisive spot kick and send his team into a last four meeting with hosts Australia on Tuesday.
The winner of that semi-final in Newcastle will meet South Korea or Iraq, who also progressed on penalties on Friday, to decide the continental champions back at Stadium Australia on Jan. 31.
It was the first time Japan had been knocked out before the last four since 1996, which was also the last time UAE reached the semi-finals before going on to lose the final as hosts.
"Sometimes you have to play with your heart and we worked very hard to win this game," said UAE coach Mahdi Ali.
"We fought for 120 minutes and I think we deserved to reach the semi-finals."
Substitute Gaku Shibasaki had earlier briefly saved the blushes of the Samurai Blue by equalising nine minutes from the end of normal time after Ali Ahmed Mabkhout had given the Gulf nation an early lead with his fourth goal of the tournament.
Mabkhout's powerful shot into the corner of the net after seven minutes was the first goal Japan had conceded in Australia and stunned the blue-shirted, drum-thumping band of their supporters behind the goal into a rare silence.
Japan had not won the Asian Cup four times in the last six tournaments by panicking, though, and they continued to press forward after the goal with the neat inter-passing game that won them three from three in the group stage.
As they had in those games, however, Japan failed to convert possession into clear-cut chances, Takashi Inui wasting the best of them in the first half by directing his far post header straight at goalkeeper Majed Naser.
Japan had kept danger man Omar Abdulrahman quiet before halftime but the languid midfielder nearly helped his side double the lead four minutes after the break with a delightful flick into the box that Mabkhout just failed to control.
Inui had been replaced by Yoshinori Muto at halftime and the substitute had two chances to make a quick impression but flashed a shot wide before also failing to hit the target with a free header.
That set the template for the next half an hour of the match.
The UAE goal was under almost permanent siege but a combination of stout defending and misfiring Japan forwards kept the underdogs ahead until Shibasaki lashed the ball into the net from the edge of the area after a one-two with Keisuke Honda.
Having been handed a lifeline, Japan looked determined to finish the tie in normal time but continued to waste a string of chances and the profligacy continued into a strangely passionless extra half an hour.
Honda sent the opening spot kick high over the bar but Khamis Esmaeel did the same with the UAE's third penalty and the shootout went to sudden death.
"Football is a game of scoring goals and we only managed one which is why it finished 1-1," said Japan's Mexican coach Javier Aguirre.
"I think our opponents played the match of their lives to get that result and I congratulate them."
(Editing by Martyn Herman/Sudipto Ganguly)
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