Mohamad Al Zino gave Syria a 15th-minute lead but Ali Dyab's own goal levelled the Group B contest and the defender then failed to deal with Amer Shafri's long goal-kick which allow Odai Al Saify to grab the winner in the 59th minute.
Jordan had a chance to make a dream start inside the first minute when Amer Deeb played in Hasan Abdel Fattah, but he slid his effort wide of the post.
Syria then took the lead after quarter of an hour when keeper Shafi could only parry Sanharib Malki's angled shot into the path of Al Zino and the forward lashed the ball into the back of the net from six yards.
Al Zino was then guilty of a poor miss when he directed a free header from Malki's cross way off target from six yards and it was to prove crucial as Jordan equalised in the 31st minute. Deeb swung a cross into the box from the right and some mis-communication between Dyab and keeper Mosab Al Balhous saw the defender head into his own net.
Fattah then steered a half-volley wide of the far post when he latched onto a floated diagonal ball in behind the Syrian defence as the first-half ended with honours even.
Samer Aouad called Shafi into action 11 minutes into the second period with a drive from distance after Jordan failed to clear a corner, before another defensive mix-up at the other end saw Adnan Hamad's side take the lead.
Shafi's long goal-kick was missed by everyone and a hesitant Dyab allowed Al Saify to get the other side of him before the striker stuck out a leg to knock the bouncing ball past the onrushing Balhous and into the net.
Moayad Abukeshek hit the side netting following a driving run from the left flank with eight minutes to go as Jordan looked the more likely to add to their tally and they duly closed out the victory that sent them into the last eight.