On a day where each match featured four goals, Jordan's thumping victory moved them to the top of Group E - above South Korea who beat Bahrain 3-1 earlier on Monday.
Jordan's Mahmoud Al-Mardi put his hand up for an early contender for goal of the tournament when the winger gave his side the lead with a shot from outside the box that floated over the keeper and into the top corner at the far post.
Musa Al-Taamari doubled their lead from the spot after a penalty was awarded for a foul on Yazan Al-Naimat following a VAR review while Al-Mardi made it 3-0 when he scored his second from a tap-in after being set up by Yazan Al-Naimat.
Al-Taamari grabbed his second when he lobbed the keeper in the 85th minute to complete the rout.
Like Malaysia, Indonesia were also making their return to the Asian Cup for the first time since 2007 and though the Southeast Asian side were able to hold their own against Iraq for 45 minutes, they ran out of gas in the second half.
Iraq's Mohanad Ali scored first when he was through on goal with just the keeper to beat but Marselino Ferdinan equalised after some fine work form Yakob Sayuri, who skipped a challenge and crossed the ball into the six-yard box for an easy goal.
However, Iraq burst Indonesia's bubble late in added time just before the interval when Osama Rashid scored from close range after the keeper spilled a save.
Substitute Aymen Hussein then won a header in the 75th minute and volleyed home from the edge of the six-yard box to make it 3-1.
Iraq are second in Group D behind four-times champions Japan, who beat Vietnam 4-2 on Sunday.
