Held to a 1-1 draw after extra time, Japan survived three times in the shootout after missing their first two spot kicks. They went through when defender Bashar Bani Yaseen fired Jordan's seventh kick wide.
Japan, who had to overcome a hostile crowd of 52,000 in Chongqing, play Bahrain in the semi-finals on Tuesday.
However, their victory was marred by controversy after Japan coach Zico and his coaching staff held up Jordan's second kick to protest about the condition of the turf around the penalty spot.
Shunsuke Nakamura and Brazilian-born Alex had blazed over before the shootout was delayed by the Japanese bench, provoking a furious row between players, coaches and match officials.
Malaysian referee Subkhiddin Mohd Salleh surprisingly ordered the teams to switch ends, to the obvious annoyance of the Jordan players and coach, Mahmoud Al Gohary.
"We have never seen a referee switch ends for penalties just because he received a demand from the other team," fumed his assistant, Alaa Nabil.
"We
Jordan still had three chances to win the match on penalties but goalkeeper Yoshikatsu Kawaguchi kept Japan alive with superb saves from Haitham Al Shboul and Anas Al Zboun.
FAIRYTALE RUN
Bani Yaseen then pulled the decisive kick wide to end Jordan's fairytale run in their first Asian Cup appearance.
Cheered on by Jordan's King Abdullah, they had stunned Japan in the 11th minute, left-back Khaled Sa'ed whipping in a cross for striker Mahmoud Shelbaieh to power a header past Kawaguchi.
But Japan struck back three minutes later when a Nakamura free kick was fumbled by goalkeeper Amer Shafi Sabbah, leaving forward Takayuki Suzuki with a simple tap-in.
Zico, meanwhile, said it had been Japan captain Tsuneyasu Miyamoto's decision to lobby the referee to switch ends during the penalty shootout.
"It was not my decision," said the Brazilian. "Miyamoto decided to protest after watching what happened for the first three penalties."
Abdullah Abu Zema had no trouble converting Jordan's first kick after watching Nakamura miss badly.
