Two second-half goals from recalled striker Adam Boyd helped Orient end a run of three consecutive home defeats.
Swindon took the lead when Anthony McNamee broke clear and his shot was deflected past goalkeeper Glenn Morris for an own-goal by Alton Thelwell.
The home side hit back from the penalty spot through Boyd after Miguel Comminges had brought down Wayne Gray.
And Boyd grabbed the winner four minutes later when he headed home a JJ Melligan cross.
Leyton Orient: Morris, Chambers, Thelwell, Saah, Palmer, Melligan, Terry, Thornton, Demetriou, Gray (Ibehre 78), Boyd (Barcham 84). Subs Not Used: Nelson, Corden, Fortune.
Goals: Boyd 51 pen, 55.
Swindon: Brezovan, Jack Smith, Ifil, Aljofree, Comminges, McGovern, Easton, Allen (Zaaboub 25), McNamee (Ashikodi 81), Sturrock, Cox. Subs Not Used: Phil Smith, Vincent, Morrison.
Goals: Thelwell 20 og.
Att: 3,082
Ref: Dean Whitestone (Northamptonshire).
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