Swindon caretaker boss David Byrne got a win in his last game in charge before Danny Wilson takes over as manager.
The Robins took the lead after 43 seconds when Lee Peacock fired a fierce drive past home keeper Glenn Morris.
Jack Smith eventually doubled Swindon's advantage from the penalty spot on the hour mark after Alton Thelwell had been penalised for handball.
In a rare spell of Leyton Orient pressure defender Tamika Mkandawire reduced the arrears with a header.
Leyton Orient: Morris, Purches, Thelwell, Mkandawire, Granville (Morgan 73), Melligan (Jarvis 65), Chambers, Thornton, Demetriou, Boyd, Parkin.
Subs Not Used: Jones, Saah, Cave-Brown.
Booked: Mkandawire, Melligan, Granville.
Goals: Mkandawire 79.
Swindon: Brezovan, Jack Smith, Ifil, Kanyuka, Timlin, Easton, Nalis, McGovern, Peacock, Sturrock (Pook 88), Cox.
Subs Not Used: Phil Smith, Corr, McNamee, Morrison.
Booked: Timlin, McGovern, Peacock.
Goals: Peacock 1, Jack Smith 61 pen.
Att: 4,349 Ref: Jarnail Singh (Middlesex).
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here