Town’s win moves them into second place in League One with 21 points from 10 matches played.
Swindon kicked off with one change in their line up from the previous match at Barnsley with Andy Williams starting in place of Jonathan Obika who missed out through injury.
Town were being backed by a good away following of 1220 fans in the crowd of 5422 and made a bright start and earned a corner in the 5th minute when Amari'i Bell’s cross was deflected behind but they lost the initiative when Michael Smith was penalised for pushing when the ball was crossed.
Chris Dagnall wasted a superb chance for Orient when he found himself with plenty of space on Town’s left flank in the 8th minute but he blasted into the side netting.
Shortly afterwards Jobi McAnuff was cautioned for a late challenge on Nathan Thompson when challenging for a loose ball.
Town responded with some neat passing between Luongo and Byrne who advanced into the penalty area before sending in a low cross which the O’s keeper Woods took cleanly.
There was a major scare for Town in the 16th minute when two Orient players including McAnuff appeared well offside and he crossed to Dean Cox who fired in a shot at goal from the angle of the penalty area but Nathan Thompson headed the ball clear.
Former Town player Scott Cuthbert was lucky not to be shown a yellow card for a late challenge near the left touchline only to be lectured by the referee Tim Robinson and when the ball was crossed to the back post, Michael Smith could only head straight at a defender and eventually the home team were awarded a goal kick for a deflection off Luongo.
Dean Cox was allowed plenty of space in midfield in the 23rd minute but fortunately his attempted lob over Foderingham only ended up with the ball flying over the goal.
Town were awarded a corner in the 24th minute which was taken by Bell but the ball was temporarily cleared by the O’s only for it to be drop back to Bell who crossed for Williams to head goalwards but his effort was cleared.
Orient’s Dagnall went close with a rasping shot in the 28th minute after picking the ball up in midfield but his effort was deflected at the expense of a corner and when that was taken, Jay Simpson eventually fired into the side netting after the ball had pinged around the penalty area.
However Town counterattacked strongly and went ahead in the 29th minute through Michael Smith who collected the ball near the penalty spot and sidestepped a defender to fire past Woods to lift the volume around the massed ranks of over 1,000 Town fans.
Orient was awarded a corner in the 35th minute when Bell intercepted a cross but Louis Thompson headed the ball clear.
Town were continuing to play their patient passing game in contrast with Orient’s more direct style and were awarded a corner when Baudry flicked a Byrne cross behind in the 39th minute but the ball was cleared.
Town gifted Orient a good chance to equalise when Foderingham’s flick over the top of an onrushing attacker left Jack Stephens unable to control the ball quickly and he was penalised for handball by the referee on the edge of the penalty area. Up stepped Orient midfielder Dean Cox but his effort struck the defensive wall and the ball went out for a corner which was cleared to Luongo who charged downfield to launch a good attack.
Nathan Byrne went close at the start of the two minutes of added time with a good shot from the edge of the area but his effort was deflected for a corner taken by Byrne and he eventually ended the move with a wayward shot.
There was no other action to report before the half time whistle was blown to end a good half for Town who went in one nil up having withstood some strong Orient pressure.
Orient kicked off but were absolutely stunned in the 47th minute when Swindon doubled their lead with a fantastic team goal shaped by Luongo who passed to Smith on the right wing and his inch perfect box into the penalty area saw Nathan Byrne fire home under Woods.
The home side went narrowly close to pulling a goal back in the 49th minute when Dagnall fired with wide with a half volley from the edge of the penalty area.
Dagnall was replaced shortly afterwards by former Town loanee Darius Henderson as Orient caretaker manager Kevin Nugent tried to change his team’s fortunes.
Swindon were awarded a free kick in the 57th minute when Byrne was tripped from behind and when the ball was crossed, Michael Smith was unable to get any power behind his header and the keeper gathered cleanly.
Swindon withstood a period of pressure before Amari'i Bell found himself with time and space to shoot in the 64th minute but Woods parried his effort at the expense of a corner.
Mathieu Baudry was cautioned in the 66th minute for a challenge from behind but Town wasted the resulting freekick.
Dean Cox threatened briefly with a header from a free kick awarded in the 68th minute but Foderingham took the ball cleanly before launching another attack.
Shaun Batt replaced Jay Simpson in the 75th minute and he took up his position up front for the home side.
Orient were awarded a free kick in the 76th minute for a late challenge which led to Batt heading straight at Foderingham who caught the ball cleanly and Batt was again denied by the Town keeper who did well to parry a goal bound shot before knocking the ball out for a corner.
Another Town counterattack led to a corner when Williams was tackled in the penalty area but after a short corner routine the ball eventually went out for a goalkick.
Nathan Byrne put in another strong run into the penalty area before being tackled at the expense of a corner but the initiative was lost when Town were penalised for offside.
Orient gave Town a scare after a patient build up when Romain Vincelot headed wide from 12 yards with Foderingham beaten in the 84th minute.
Jake Reeves replaced the hard working Andy Williams who received a good round of applause in the 86th minute from the 1220 Town fans present for his efforts including the opening goal.
The Town fans were in good voice as the match entered the 5 minutes of added time but there was added excitement when Dean Cox poleaxed Nathan Byrne which led to several players getting involved in a pushing match. Order was eventually restored after the match officials had consulted each other and yellow cards shown to Yaser Kasim and Henderson and Cox.
Orient pulled a goal back in the 6th minute of added time through Henderson’s header from close range to give the Town fans the jitters but they managed to hold on for another good away victory to move onto 21 points.
The Robins players received great applause from the travelling faithful in recognition of their efforts at a ground where Town have previously struggled to win in recent years.