Ajay Leitch-Smith could have snatched the three points for Alex with a shot which crashed against the woodwork while Joe Garner went closest for Carlisle, hitting the post midway through the second half of Tuesday night's League One clash.
Crewe dominated early on and Matt Tootle's ball into the box set up Max Clayton for an early sight of goal, but the striker screwed his shot wide,
Carlisle finally woke up in the 39th minute when teenage midfielder Brad Potts hit a superb first-time volley from 30 yards which Alan Martin was at full stretch to beat away.
Carlisle looked to former favourite Garner, back on a 28-day loan from Watford, for inspiration as a half-time substitute for Jake Jervis and he almost produced the goods with a glancing shot from Danny Cadmarteri's cross, only to see the ball come back off the right-hand post.
Leitch-Smith went equally close for Crewe with a fine 70th-minute strike which struck the underside of the bar.