Colin McMenamin scored the only goal as Shrewsbury won away for the first time this season.
McMenamin converted from the penalty spot after just three minutes following a rash challenge by defender John Mackie on Dave Edwards.
Orient pushed for an equaliser and Jamie Tolley made a goal-line clearance to keep the Shrews in front.
The Shrews should have doubled their advantage late on but McMenamin shot tamely with only Glyn Garner to beat.
Leyton Orient: Garner, Miller, Zakuani, Mackie (Barnard 51), Tudor, Simpson, Easton, Keith, Palmer (McMahon 45), Steele, Alexander (Echanomi 68).
Subs Not Used: Dolan, Morris.
Shrewsbury: Hart, Whitehead, Ashton (Hogg 85), Walton, Hope, Tolley, Sorvel, Denny, Edwards (Sharp 57), Langmead (Herd 74), McMenamin.
Subs Not Used: Smith, Thompson.
Booked: Sorvel, Ashton.
Goals: McMenamin 3 pen.
Ref: I Williamson (Berkshire).