It was the perfect home start for new boss Geraint Williams, as he saw his new side clinch only their third home win of the season and push Crewe deeper into the relegation mire.
In an eventful first half Orient's top-scorer Adam Boyd shot wide before Crewe responded and should have gone ahead when John Brayford's cross was headed wastefully wide by Shaun Miller.
But it was the home side who made the breakthrough on ten minutes when Boyd's ball cut open the Crewe defence and full-back Purches latched onto it and cut in before rifling the ball past John Ruddy for his third goal of the season.
Former Orient player Billy Jones went close at the other end while Orient's on-loan signing Scott McGleish was denied by Ruddy after some good approach play.
Orient were forced into an early re-shuffle when Dean Morgan replaced the injured Boyd and as Crewe came back into the game Tom Pope saw a header ruled out for offside and Clayton Donaldson also went close.
But Orient also looked good going forward and Purches went close to adding a second with a superb volley that Ruddy brilliantly tipped away.
After the interval Orient took control with some neat passing football and Jason Demetriou went close to stretching their advantage.
The midfielder went close again when he raced clear of the Crewe back-line but saw his shot saved by the visiting goalkeeper.
The home side wasted a glorious chance to give themselves some breathing space when 11 minutes from time Morgan's cross found McGleish six-yards out, but somehow the striker rolled the ball the wrong side of the post.
Orient were almost made to pay when Crewe substitute Byron Moore fired over. The home side held on for a crucial win.