Paul Musselwhite then had to save from Matt Brazier before Jabo Ibehre made it 2-0 just 2 minutes after Thorpe's goal. Stuart Green failed to clear, allowing the Orient forward to turn and shoot past Musselwhite, doubling the home side's lead.
Ibehre had another chance just before half time but headed wide from close range.
Ryan Williams and Carl Regan were brought on at half time, but City had nothing to show for their early pressure in the second half, and Ibehre had another opportunity for the O's but shot wide.
Stuart Elliott had a shot saved but City rarely tested Scott Barrett, and even with Lawrie Dudfield on the pitch for the last 15 minutes were unable to find a way back as Orient held on to their 2-0 lead.
City line-up (4-4-2): Musselwhite; Joesph, Anderson (Dudfield 75), Delaney, Holt; Green, Ashbee, Melton (Regan 45), Elliott; Alexander (Williams 45), Webb.
Un-used subs: Harvey, Jevons.