Goals from Abdallah Deeb, Anas Bani Yaseen and Ahmad Hayel consigned the hosts to their third straight defeat and sent them to the bottom of the Group A table.
With nine points still to play for, Singapore can still mathematically qualify for the playoffs - but will need to win all three of the remaining games to have any chance - a tall order given that they have to travel to Jordan and Iraq for two of those games.
It was the home side that fired the first salvo on Tuesday, as Young Lions captain Hariss Harun found Fazrul Nawaz on the edge of the area, but the striker's shot flashed just wide of Amer Shafi's left post.
After a poor performance in the 2-0 friendly win over Philippines on Friday, it was an encouraging start for Radjoko Avramovic's men. However, Jordan settled down after the opening five minutes, and started stroking the ball around nicely on the plastic turf, with Abdallah D. dictating the early play for the visitors.
The forward carved the first opportunity for Jordan, cutting in from the left before firing a stinger that Singapore keeper Izwan Mahbud did well to beat away. That shot set the tone for the next 10 minutes or so as Jordan pressed for the opener.
With Deeb combining well with Odai Al Saify and Hasan Abdel Fattah, Jordan dominated in the final third - especially as the Singapore backline repeatedly backed off. Anas Bani Yaseen found plenty of space just outside the box and warmed Izwan's hands.
But worse was to come.
Al Saify's neat through ball put in Ahmad Hayel, whose first time cross found Abdallah D. unmarked right in front of Izwan. The forward made no mistake in finding the net from six yards out. Jordan almost went two up a couple of minutes later, with only a full-stretch dive from Izwan preventing an Al Saify shot from nestling in the net.
To their credit, Singapore refused to let their heads drop - holding the ball for long periods of time and probing for weaknesses in the Jordan backline. The patient build-up play resulted in two absolutely gilt-edged chances - both of which went abegging, much to the chagrin of the 3,799 fans at Jalan Besar.
In the 20th minute, Safuwan mistimed his jump horribly when presented with a free header inside the box from a Shahril Ishak corner and about 15 minutes later, Fazrul Nawaz scuffed his shot after being found free on the right by a flat cross from Shaiful Esah.
Those two chances, combined with some threatening play down the right, gave the home supporters hope of an equaliser as the sides went in at the break. But it was not to be.
Jordan came out the more charged of the two sides after the interval and nearly doubled their lead within the first minute of the restart as Fattah's header smashed off the crossbar. One could sense a goal coming, and it duly did in the 54th minute. Safuwan conceded a foul inside his own half and from the resultant free-kick defender Yaseen flicked the ball through Izwan's legs and into the net.
While the response to the first goal had been encouraging, the second completely took the wind out of Singapore's sails.
The physical and mental effort of having given their all through the opening hour without any reward seemed to have sucked the strength out of them - as Jordan completely took over the match.
The Singapore defence was being cut open at will - and the third goal, when it came, had a sense of inevitability about it. Hayel got the ball just outside the area, drifted in while holding off two defenders before unleashing a low, left-footed strike which found the bottom corner of Izwan's goal.
But even as the Singapore faithful headed for the exits, there was time for some more drama at the death. The home side won a free-kick right outside the area and caught the Jordanian defence completely unaware by taking it quickly.
Ishak ran on to it and side-footed it home to finally give the fans something to cheer about. Confusion reigned however, as the linesman beckoned the referee to come over and after a short deliberation - declared that Ishak had been offside.
Singapore could consider themselves unlucky as television replays showed the player level with the backline - and that decision galvanised them for one final assault on the Jordan fortress. Substitute Muhammad Khairul found himself through on the right - and his angled shot was well saved by Shafi - denying fans the solace of even a consolation strike.
Speaking at the post-match press conference, Singapore Assistant Coach V.Sundramoorty “I think we did not take our chances and it is important at this level to convert chances when you have them. I think with time, with these young boys, we have a future. We have three games left and mathematically, if we get maximum points from the remaining games, we will still have a chance.”
Adding on, he said “We are developing this team and they are a young team. We started the game positively and should have minimised our mistakes. The players fought till the end and they tried their best.”
Jordan’s Head Coach Adnan Ahmad “I am very happy that the team played well and got a good result. And we are closer to the fourth round now. We respect the Singapore team and that’s why we played a good game. The players deserve the result.”
Singapore Starting XI: Izwan Mahbud (GK), Shaiful Esah (LB), Safuwan Baharudin (CB), Daniel Bennett (CB), Juma'at Jantan (RB), Hariss Harun (CM), Shi Jiayi (RM), Hafiz Rahim (MF), Shahril Ishak (LM), Fazrul Nawaz (FW), Aleksandar Duric (FW)'
Subs: Isa Halim for Shi Jiayi (45'), Shahdan Sulaiman for Hafiz Rahim (45'), Khairul Nizam for Fazrul Nawaz (61')
Jordan Starting XI: Amer Shafi (GK), Bashar Bani Yaseen, Shadi Abu Hashhash, Basem Fathi, Anas Bani Yaseen, Baha' Abdelrahman, Khalil Zaid Kh. Baniateyah, Hasan Abdel Fattah, Ahmad Hayel, Abdallah Deeb, Odai Al Saify