It was another disappointing display by the Saudis, who showed no improvement under coach Nasser Al Johar after he stepped in to replace sacked Portuguese Jose Peseiro following the shock opening defeat by Syria.
"I respect Al Johar and the Saudi team but our winning over the Saudi team is a big accomplishment for the Jordan team," coach Adnan Hamed told reporters.
"We played in a realistic way but we did not win with luck. We played very well and our players produced a very good performance."
A woeful opening half where neither side appeared to want to hold possession ended with another mistake when Abdullah was caught out by the swirling breeze at a cold Al Rayyan Stadium, with many of the 17,349 crowd in jackets, gloves and hats.
Three minutes before half-time, Jordan's Bahaa Abdelrahman floated a hopeful, inswinging ball in to the penalty area which sailed over Abdullah, who had stepped of his line to come for the cross, and in to the corner of the goal.
"He (Abdullah) may have made a mistake and the mistake he has done is common in the world of football," Al Johar told reporters.
Hamed acknowledged the good fortune: "We were lucky to score and in the second half we maintained our advantage and played very well."
The three-times champions improved after the break, roared on by their passionate supporters but struggled to find a breakthrough with their captain and leading goal threat Yasser Al Qahtani unable to get into the game.
The Saudis went close on a number of occasions in the final stages but the 107th ranked Jordan side held firm, their players desperately throwing themselves in front of Saudi efforts on goal.
Defeat was greeted by a chorus of boos from angry Saudi supporters as the Jordan players ran to their fans to celebrate.
The result left Saudi Arabia bottom or Group B without a point from two games with Jordan on four from two matches.
"We didn't fail," said Al Johar, who answered questions believing his side were still in the tournament.
"The Jordan team played defensive throughout the game and we could not reach the goal to score and we were unlucky.
"The Saudi team played very well considering the circumstances. We missed a couple of chances to score and the Jordanian goal was luck."
