It was another disappointing display by the Saudis, who had put coach Nasser Al Johar in charge after sacking Portuguese Jose Peseiro following the opening match defeat by Syria.
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 halftime, 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.
Saudi Arabia 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 made four changes from the side that embarrassingly lost to Syria, including bringing in midfielder Taiseer Al Jassam, who came off the bench to grab his team's solitary goal in the Syria debacle.
Jordan, who came within moments of defeating Japan in their opener but had to settle for a 1-1 draw, were missing captain and central defender Hatem Aqel, who was stretchered off after injuring his right knee against the Japanese.
Saudi Arabia should have been ahead within a minute of the post-Peseiro era, but defender Osama Al Harbi completely missed his header right in front of goal when an inswinging corner somehow made it through a packed penalty box.
The Saudis were in control early on at the Al-Rayyan Stadium, cheered on by a sizeable travelling support decked out in green.
Striker Naif Hazazi, one of the four new players drafted in, was at the centre of everything.
On 16 minutes his goal-bound header was clawed away by Jordan keeper Amer Shafi, and moments later the bouffant-haired Hazazi blazed just wide.
But three minutes before half-time Jordan got the goal against the run of play. Baha Abdelrahman was left unchallenged and given all the time in the world to loft over a cross that inadvertently curled into the net.
It was a moment of horror for keeper Waleed, who totally misjudged the flight of the ball.
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