The goals came from Yousef Ahmad and four from Hamza Al Dardour while Palestine's goal came late in the game from Jaka Hbaisha.
The win put Jordan level on three points with holders Japan and Iraq, who meet later on Friday, ahead of their tough Group D finale against the Samurai Blue
Palestine are now eliminated after two losses.
In the 33rd minute Jordan opened the scoring through Mohammad who found the back of the net with a stunning shot.
A minute later Hamza got the first of his four goals and then another in first-half stoppage time with a volley past goalkeeper Ramzi Saleh.
Hamza completed his hat-trick in the 75th minute when he picked up the ball in the Palestine half and ran forward at pace before sliding the ball home to complete his hat-trick to make the score 4-0.
He then scored his fourth in the 80th minute slipping in behind the tired Palestine backline to convert Oday Zahran's cross from the right.
The Palestinians scored a first-ever Asian Cup goal when midfielder Jaka Hbaisha completed a set piece in the 85th minute to make the final score 5-1.