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Mousa Suleiman scored one goal and made another for Tareq Khattab as Vital Borkelmans' side ran out comfortable winner at Khalifa bin Zayed Stadium on Friday (AEDT).
Having beaten Australia 1-0 in its Group B opener Jordan is assured of qualification while Syria - yet to score in the tournament - will need a result against the Socceroos.
After a slow start to the game Jordan took the lead in the 26th minute.
Yasen Bakheet tricked his way into space on the left wing and found Yousef Rawshdeh with a low cross, with his shot stabbed in from close range by Suleiman.
The same combination almost provided a quickfire second but Suleiman's shot bounced over the crossbar.
Suleiman then turned provider in the 43rd minute, his corner powered in at the near post by centre-back Khattab.
Syria missed a golden chance to get back in the game when Omar Khrbin headed wide a Fahad Youssef cross in the 50th minute, before Syria's Ahmad Al Saleh narrowly avoided an own goal.
Omar Khrbin wasted a string of opportunities to open Syria's Asian Cup account, while the lively Bakheet went close to adding a third for Jordan.
But Borkelmans' men can now start thinking ahead to the next round after booking qualification.