A lively start from the home side resulted in their first opportunity after nine minutes when Danny Whitaker's corner reached George Pilkington at the back post but his thumping header was parried by Ben Williams.
Crewe found their feet soon enough and tested Joe Anyon a minute later when a long ball up field supplied Simon Church but, despite beating Ashley Westwood, the forward's shot was comfortably held.
Whitaker was proving to be a menace from set pieces and asked more questions of the Crewe defence when his free-kick from the right dipped inches over the crossbar in the 23rd minute.
The visitors almost took the lead 10 minutes before the break when a half-cleared corner found Byron Moore on the edge of the box but his volley sailed past Anyon's left post.
Impressive defending from Julien Baudet kept the scores level three minutes after half-time when David McGoldrick had a superb shooting chance from close range but a last-ditch challenge sent the ball for a corner.
Seconds after having a penalty shout turned down, Luke Rodgers came close to scoring against his former employers but the slightest of touches from Williams turned over his 25-yard effort.
Elliott Bennett broke Valiant hearts in the 76th minute when Moore's charge down the right supplied the substitute with the ideal opportunity to slot the ball confidently into Anyon's bottom right corner.
Sinnott's men almost had themselves an equaliser a minute later when Paul Harsley's low cross was directed goalwards by Mark McGregor, but unfortunately for him it fell onto Williams' right post.
The Railwaymen should have wrapped up the result in style during the dying stages but some superb goalkeeping from Anyon stopped short Church's one-on-one advance.