Goals from Thaer Bawab, Ahmad Hayel and Yousef Rawshded also secured qualification for Al Nashama with one game left, as they clinched second place behind Oman in Group A.
Lions coach Bernd Stange opted to deploy Safuwan Baharudin in defensive midfield, with Khairul Amri and Hafiz Sujad flanking lone striker and captain Shahril Ishak.
The visitors made their intentions clear straight from kick-off as they effectively played with four forwards and pressed high up the pitch.
Singapore custodian Izwan Mahbud had to be alert to smother a few dangerous crosses, with his defenders bailing him out with two crucial blocks in the opening stages.
Bawab dragged a shot wide in the 12th minute as the Lions struggled to get out of their half, with Izwan then blocking well from Ahmad Hayel’s fierce effort.
Safuwan fired a 30-yard free-kick straight at Mohamad Shatwani in the 22nd minute, with Oday Zahran forcing Izwan to to tip away his 25-yard set-piece attempt two minutes later.
The hosts threatened again from the dead ball as half-time approached. Safuwan climbed well to knock back Zulfahmi Arifin’s corner to the far post, but the angle was too tight for Baihakki Khaizan to get his header on target.
But having flattered to deceive since their bright opening exchanges, Jordan then broke the deadlock two minutes before half-time.
After Shakir Hamzah had nudged Hayel on the edge of the box, a clever free-kick routine saw Bawab curl a well-placed strike into the far corner with Izwan rooted to his line.
Things quickly got worse when Baihakki was shown a straight red card 60 seconds later for allegedly hitting Mossab Al-Laham in an off the ball incident.
There was still time for Zulfahmi to put yet another dangerous delivery into the box as Shahril flicked the ball on for Safuwan at the far post, with Khairul Amri failing to convert the resulting cross-shot.
A chorus of boos serenaded referee Tan Hai at the half-time whistle, who had to be led to another exit after Singapore coaches Lee Bee Seng and Nazri Nasir briefly confronted him. The latter was subsequently banished to the stands for the second half.
Hariss Harun dropped back to fill the void in central defence after the break, as the Lions went close to equalising five minutes into the half.
Shahril swung a free-kick to the far post for Shakir, whose knockdown was miscued by Safuwan. The ball bounced free for Afiq to shoot on the turn, with the strike fizzing past the post.
Shatwani was soon scrambling across his goal again, as Zulfahmi’s long-range grounder went just wide.
But poor defending allowed Jordan to double their advantage in the 59th minute. Left with all the time and space in the box, Hayel easily headed in Al-Laham’s corner from close range.
Shakir did superbly to prevent a third when he hacked Bawab’s shot off the line after the latter had rounded Izwan, with Jordan going down to 10 men soon after as Hayel copped a needless second yellow for tripping Safuwan.
The home side were thrown an unexpected lifeline on 84 minutes when Baha Abdel-Rahman was harshly adjudged to have blocked Safuwan’s cross with his arm. Amri had no trouble sending Shatwani the wrong way from the spot for his second goal of the qualifiers.
The Jalan Besar crowd encouraged the hosts forward for an equaliser, but it was Jordan who sealed victory inside the four minutes of added time.
Substitute Rawshded clinically finished past Izwan after Rajaei Hasan sent him clear, leaving Singapore with nothing to show for despite a determined performance on the night.