Tha'er Al Bawab opened the scoring in the 42nd minute of the Group A clash with a curling effort after a well-worked free kick on the edge of the penalty area.
And Singapore suffered another blow before the break as Baihakki Khaizan was given his marching orders following a needless barge on an opponent.
Ahmad Hayel rose well to head home a corner just before the hour mark as Jordan edged closer to a guaranteed spot at next year's event in Australia.
However, those hopes suffered a setback 10 minutes later when goalscorer Hayel was sent off for a second bookable offence.
Khairul Amri reduced the deficit from the spot in the 83rd minute as Jordan were penalised for a handball in the box, but the hosts' revival was short-lived.
Yousef Al Rawashdeh completed a quick attacking move for Jordan in stoppage time to put the result beyond doubt.
The victory lifts Jordan to within two points of leaders Oman with one fixture left to play, while Singapore need an unlikely combination of results to potentially qualify as the best third-placed side.
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