Orient came out on top from one of the season's most one-sided games, as Williams' team reaped yet another win on the road to guarantee League One safety.
Jason Demetriou returned with a bang from suspension by opening the scoring in just the second minute. From 20 yards out he latched onto Wayne Gray's lay-off and placed a swerving shot high into the net.
His strike left Phil Smith in goal for Swindon rooted to the spot, admiring the view in no-man's land.
Demetriou's goal came almost as quickly as Swindon's Boxing Day opener had done at Brisbane Road.
But when the dust settled on it, on came Swindon.
Orient fought a rear guard action almost the entire match as the back four fended off a flurry of Robins attacks. There were rare forages forward, as Wayne Gray, Scott McGleish and later Simon Church fed on crumbs.
Anthony McNamee posed a persistent threat down the left flank for Swindon which drew Melligan in from midfield to help Purches nullify.
25 goal Simon Cox was an ever-present hazard to Orient's lead, but there was plenty else for Geraint Williams' men to think about.
Jamie Jones in goal for the O's produced another string of top saves during a busy afternoon.
He tipped over a goal bound swerving strike from his namesake Owain Jones on 16 minutes, and was always solid the numerous times he had to come and collect high crosses.
The second half brought more of the same, as Purches, Mkandawire, Spence, and Daniels in defence continued to earn their corn as they chased, harried, and intercepted the roving host's.
Substitute Simon Church headed wide a rare scoring chance on 63 minutes, this time from a corner.
McNamee's exit did not bring rest for the O's defence and Daniels had his hands full in substitute Lloyd Macklin who churned up the turf down the flank, and dealt well with the nippy winger.
An equaliser always seemed about to come and the County Groung crowd grew more restless. Paynter rattled the cross-bar in a goal-mouth scramble in the 53rd.
And Swindon continued to turn the screw as the clocked counted on. The Swindon half became more and more of a foreign land to Orient, and their defensive efforts more desperate.
Paul Terry impressed with his industry.
Orient lived by the skin of their teeth, or in the 78th minute, by the width of Jones' head. Cox's effort re-bounded off the post onto the keeper. Jones was equal soon after to his header.
With a minute of the 90 left, Daniels put a vital foot in the way of Tudor Jones' shot from eight yards out as the stands readied to erupt.
The footballing Gods are with Orient right now, and the club can plan for another League One campaign.
Attendance: 7,735 Jones, Purches, Mkandawire, Melligan, Gray, Thornton (Smith 54), Terry, (booked 34m,) Demetriou, Daniels, Spence, McGleish (Church 54.) Subs: Morris, Saah, Boyd, Smith, Church.
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