Four straight PDL wins for Blues, without conceding a goal, take them top of the divisionbcfc.com
Miguel Fernandez drilled in what proved to be the winner from an indirect free-kick after Crewe were penalised when the goalkeeper handled a backpass.
Jack Concannon tapped the ball sideways for Fernandez, whose left footer squeezed past the string of Crewe defenders onrushing from the goal line.
Usually it is harder to score in these close-range situations, but Fernandez was perfectly precise in directing the ball low just inside the post from about 10 yards.
Blues had a few scares thereafter as they looked to see out victory and a fourth straight success in the PDL - with no goals conceded, for good measure.
But overall they were worthy of the success, as for the majority of the match they dominated possession, probed the most and created the better openings, making light of a heavy, cloying surface.
Crewe were first to threaten when Ryan Burke took evasive action to clear, at the front post, a difficult cross from the left; the ball only just avoiding his own goal.
But Blues then settled into their groove and intelligently moved the ball and their opponents around to good effect.
Fernandez dragged a left footer wide after taking on the ball from Jayden Reid, who caused problems for the Crewe defence.
He perhaps should have the hit the target, but 'keeper David Richards were certainly kept on his toes for the remainder of the first-half.
He stopped Concannon glancing the ball past him from close range after a searching pass behind by Burke, and he was almost beaten by at attempt from Reid, which dipped and bobbled just past the post.
In the 34th minute, Fernandez was denied by a fine save, after Blues exerted a period of sustained pressure. He struck a whipped shot that Richards got fingertips to, deflected onto the post, and the ball thudded across the face of goal and stayed out.
Then Mitch Roberts got free from a left wing corner amid a blur or movement and dummy runs, but glanced his effort just wide.
After a moment of alarm at a free-kick at the beginning of the second-half, when Connor Heath almost diverted the ball in, Blues should have gone ahead.
An incisive move started with Reid holding the ball on halfway, occupying defenders, before laying it off the Kane Thompson-Sommers, who drove on from the left of midfield.
Thompson-Sommers shifted the ball to the supporting Nico Gordon on the edge of the area and the full-back checked past a challenge onto his left peg only to see his goalbound shot rebound back off the 'keeper's spreadeagled body.
Yet, from a corner, there was a let-off for the visitors when an outswinger was met by Joshua Lundstram whose header smacked midway up the near post.
In the 59th minute the game changed for the better as Blues seized the advantage.
An ill-judged backpass was parried by under pressure Richards low down, who quickly took his hands away knowing he had transgressed.
Despite a wall of red shirts filling the goal, Fernandez found the bottom corner as one of the Crewe number crucially turned his back as they charged down.
The next piece of goalmouth action was just as crucial as Moha Ramos made an outstanding save that helped earn the win.
Blues were caught over-playing deep in their own territory, possession was coughed up and Heath was played in down the middle.
With the centre-halves split, Heath looked as if he had dribbled round Ramos in the penalty area but no, the Blues 'keeper dived onto the ball and snared it away from his feet with a clean take - sharp timing, perfect execution.
With 19 minutes left and Crewe increasing their efforts, Lundstram got a lucky deflection from second phase play at a free-kick and strode forward into the box only to guide a shot wide.
At the other end Concannon prodded the ball through for subsitute Adan George but as he attempted to pull the trigger a superb recovery tackle by ravis Johnson deined him at the last moment.
Blues might have had a penalty when another substitute, Kyle Hurst, seemed to be barged over as he made his way to the byline, onto Fernandez's scooped flick.
In added-time, Blues afforded Crewe chance to load their box by conceding cheap free-kicks.
From one, Ramos came and rose high to claim a ball off the head of his opposite number Richards, who was coming in at the back post.
And in the fourth minute of the extra minutes, from a ball played back from another set-piece, Johnson powered a close range header into the back of the net only for the
linesman to flag for offside.
It would have been tough on Blues had that decision gone the other way as they were, on the overall balance of things, the more deserving and effective team, through the
Blues: Ramos, Gordon, Burke, Campbell, Redmond, Roberts, Baker (Hurst 65), Thompson-Sommers, Concannon, Fernandez, Reid (George 71). Subs not used: Forrest, Rouse.