With Iraq looking destined to move into the last eight when the clock struck 90 minutes, Jordan's Yazan Al Arab equalised in the 95th before Nizar Al Rashdan scored two minutes later with a glorious long-range effort to break Iraqi hearts.
Jordan will now face tournament debutants Tajikistan in the last eight.
"The confidence that we have made us believe we could come back and this is what we've done," Jordan coach Hussein Ammouta told reporters.
"In added time we came back, we equalised and we exploited Iraq being down one man. We have a strong mentality and we have to maintain it so we can go further in this tournament."
Jordan went ahead on the stroke of half time when Yazan Al Naimat pounced on a sloppy pass and raced past the defence.
The 24-year-old chipped the ball over goalkeeper Jalal Hassan to score before celebrating with his teammates by sitting on the turf and pretending to eat a meal.
Iraq struck back in the 68th when Saad Natiq headed home from a corner before Hussein scored eight minutes later when he controlled a cross and fired into the bottom corner.
SECOND YELLOW
The joy of scoring his sixth goal of the tournament quickly turned to shock when the referee produced a second yellow card for excessive celebrations after the striker mimicked Jordan's players and sat on the turf, pretending to eat by himself.
"In a big tournament like the Asian Cup, you cannot exclude a player after celebrating a goal. The same happened in the first half with the Jordanian players (celebrating) and the referee didn't take any action," Iraq coach Jesus Casas told reporters.
"The problem was in the timing of this red card. It took place after we had used all our substitutions, so it was a very difficult situation. We didn't have the chance to make any changes inside the pitch."
While Iraq fumed, Jordan took full advantage of the extra man and when Mousa Al-Tamari's stoppage-time effort was parried by Hassan, Al Arab was on hand to fire home the rebound.
The comeback was complete when midfielder Al-Rashdan was left unmarked outside the box and curled his shot past the keeper to spark wild celebrations in the stands among the Jordanians while the Iraqis sat in stunned silence.
Tempers flared at the post-match press conference when more than a dozen Iraqi journalists walked out while pointing fingers at Casas and shouting at him, with security and officials stepping in to lead them away when some approached the coach.
"Concerning my future, I'm calm and our goal is to qualify for the 2026 World Cup," Casas said.
"Anything might happen and I'm very calm."
