Goals from Mathieu Baudry and Kevin Lisbie either side of half-time wrapped up the points for the O's to keep their play-off hopes alive.
The Shrews started brightly with Chris Porter flashing a near-post header just wide from Dave McAllister's cross but then Orient seized the initiative.
Dean Cox and Lee Cook both tested goalkeeper Chris Weale from long range before Orient's most inventive two players combined for the Londoners' 33rd-minute breakthrough.
Orient worked a short corner and Cox's cross from the left was glanced home by the head of French central defender Baudry.
Lisbie then had the ball in the net only to be flagged offside as Orient continued to look lively, while at the other end a deflected shot from Jon Taylor was comfortably gathered by visiting keeper Jamie Jones.
Orient doubled their advantage six minutes into the second half, Lisbie coolly converting a penalty after McAllister's clumsy challenge on Romain Vincelot.
Shrewsbury rallied and Taylor and Summerfield were both denied by Jones, but Graham Turner's strugglers have now lost three successive games.