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Swans won for the first time on the road this season with a single goal from Leon Knight on 54 minutes.
It was a rollercoaster afternoon for Knight, for as well as scoring the only goal he missed a penalty and was also sent off on 63 minutes for a second bookable offence.
Justin Miller was sent off for Orient on 35 minutes for a professional foul on Darren Pratley. From the resulting penalty the O's goal-keeper, Welshman Glyn Garner, saved from Leon Knight.
Swans goal came from a free kick from Alan Tate which was headed past Garner by Leon Knight.
Leyton Orient: Garner, Miller, Lockwood, Fortune, Saah, Tudor (Barnard 35), Simpson (Ibehre 83), Easton, Keith (Connor 67), Alexander, Steele.
Subs Not Used: Morris, Corden. Sent Off: Miller (35).
Booked: Alexander, Steele, Easton.
Sent off: Miller.
Swansea: Gueret, Tate, Williams (Akinfenwa 69), Austin, Iriekpen, Amankwaah, O'Leary, Pratley, MacDonald (Way 90), Fallon (Butler 90), Knight.
Subs Not Used: Oakes, Watt. Sent Off: Knight (65).
Booked: Knight, Austin, Amankwaah, Gueret.
Sent off: Knight.
Goals: Knight 54.
Att: 4,162
Ref: A Hall (W Midlands).