Cheltenham's League One status was left hanging by a thread when their recent unbeaten run was halted at five games.
Dean Morgan was Leyton Orient's hero, drilling a neat left-footed shot into the corner after 25 minutes to register his fourth goal of the season.
Orient almost had a second after the break but Michael Townsend cleared Scott McGleish's shot off the line.
Cheltenham had a late penalty appeal waved away when Jimmy Smith appeared to handle Andy Gallinagh's cross.
Cheltenham: Brown, Lindegaard, Diallo, Townsend, Berchiche (Duff 83), Antonio (Watkins 46), Artus, Gallinagh, Connor, Hammond, Constantine (Hutton 46).
Subs Not Used: Puddy, Finnigan.
Booked: Hammond.
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Leyton Orient:
Jones, Purches (Thelwell 70), Mkandawire, Spence, Daniels, Demetriou, Terry, Smith, Morgan (Wayne Gray 78), McGleish, Church (Melligan 83).
Subs Not Used: Morris, Saah.
Booked: Daniels.
Goals: Morgan 25.
Att: 3,594
Ref: Gavin Ward (Surrey).
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