Ruel Sotiriou's first-half goal proved enough for O's to tame the Shrews at Brisbane Road.
O's were unchanged from their trip to Peterborough a week earlier, but had an early scare when Sol Brynn was forced to save Cheyenne Dunkley's header from a Malvid Benning corner.
The hosts had another let-off when Brynn denied New Zealand international Max Mata, but Brandon Cooper sent an effort just wide on 10 minutes.
And O's took the lead nine minutes later when Idris El Mizouni found Sotiriou to fire past Marko Marosi.
The Shrews went close to levelling moments later as Daniel Udoh struck his shot just inches wide of the far post, before play was held up while Sotiriou received treatment.
And after a quieter spell around the half-hour mark, as both sides battled for supremacy in the middle third of the pitch, Jordan Graham was pulled down to give O's a free-kick on 35 minutes.
Marosi flapped at the subsequent set-piece from Tom James, but the visitors were able to clear the danger.
And El Mizouni produced some excellent defensive work at the other end to prevent a Shrews one-on-one with Brynn five minutes before the break.
Tom Flanagan fired wide from range for the visitors, before Joe Pigott saw his shot hit Morgan Feeney in the box but had penalty claims for handball turned down.
Darren Pratley received the first yellow card of the game three minutes into the second half, with Cooper having his name taken soon after.
But good work by George Moncur forced Marosi into a poor kick, after O's had weathered a spell of pressure from the visitors.
Jordan Brown replaced Pratley in the first change of the day for Richie Wellens, with Shaq Forde and Aaron Drinan coming on for Moncur and Pigott in a double change just past the hour.
And Drinan produced a superb run on the right to find Forde, who teed up Sotiriou for a shot that was deflected just over.
El Mizouni dispossessed Tom Bayliss as he looked to break through, before Cooper cut inside and saw a shot deflected just wide for a corner.
But Forde picked up a yellow card before substitute Ryan Bowman's header was well held by Brynn, while James was booked for timewasting.
Dan Happe and Ethan Galbraith were sent on for Archibald and Sotiriou in another double change on 77 minutes before James saw a shot drift over the crossbar.
But Brynn had to claw an effort from the unmarked Flanagan away for a corner at the other end with six minutes left to protect the home side's lead.
Forde sent a first-time effort over the crossbar after more good work from Drinan, before excellent defending by Omar Beckles thwarted the Shrews.
And Galbraith sent an effort drifting just wide in the second minute of stoppage time after being found in the box by Forde and cutting inside.
Brown fired over before the final whistle, but O's claimed the points.
Leyton Orient: Brynn, James, Beckles, Cooper, Graham, Pratley (Brown 55), El Mizouni, Archibald (Happe 77), Moncur (Forde 62), Pigott (Drinan 62), Sotiriou (Galbraith 77). Unused subs: Howes, Hunt.
Attendance: 8,001 (including 618 Shrewsbury fans).
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