In either half they relinquished good positions to allow the visitors to take control, in the second period falling 2-5 behind.
But superb strikes by substitute Amari Miller and then Ryan Stirk inside three minutes of each other put the outcome on a knife-edge in the closing stages.
Unfortunately, though, Blues couldn't squeeze another goal to at least equalise and were left to reflect on a match that constantly swung from one end to another.
Blues were without Nico Gordon and Mitch Roberts, while Ryan Burke had earlier in the day completed his loan move to Yeovil Town.
So, with Marcel Oakely also injured, Josh Williams had to step in at right-back and Daniel Djurovic got an opening in the other full-back berth.
Blues got off to a flying start when Tate Campbell set the ball off for Kyle Hurst to embark on an elusive, mazy run at the heart of the Crewe defence. Nearing the edge of the box, Hurst unleashed a low drive that bounced in off the post with under two minutes on the clock.
But in the sixth minute Crewe were level when Regan Griffiths ran back round on himself to the left edge of the area and cracked a precise shot that gave Aaron Clayton, diving at full stretch, no chance.
Griffiths then pounced again, in the 17th minute, when Blues lost possession midway in their own half and the ball was worked into the area. Callum Ainley's attempt was parried by Clayton but only as far as Griffiths who followed up.
Blues got into some promising situations, especially down the right-hand side, but despite some dangerous crosses and balls in, couldn't find the finishing touch.
One swift move saw Adan George play the ball to Hurst who in turn prodded it through for Miguel Fernandez but, from a tight and wide angle to the right of the 'keeper, his effort rolled right across the face of goal.
Blues began the second-half well and got on level terms in the 55th, from a penalty.
It came when Williams surged forward and scooped a clever ball over the last line of defenders towards George, who was coming in menacingly. George managed to get something on it and clipped the top of the crossbar whilst in the process of being nudged over by Travis Johnson.
George dusted himself down to stick away the penalty, to the left-hand side of the 'keeper.
With their tails up, Blues then went close to regaining the lead.
From a Blues throw-in high on the right, Fernandez veered inside and clipped a curling shot that was destined for the top corner only for David Richards to palm it onto the crossbar.
Then it suddenly fell apart for Blues.
From a fierce cross from wide right by Griffiths there was Offrande Zanzala at the back post to power in a header from close range (64 minutes).
Little over 60 seconds later it got worse when Griffiths carried the ball straight down the middle from deep and played in Zanzala, who stepped aside the last challenge and prodded past Clayton.
Crewe scored their fifth in the 78th minute from a free-kick, swung into the heart of the area for Olly Lancashire to net with a soaring header.
Two minutes later Crewe had a goal disallowed for offside and then Blues began to composure themselves to stage a grandstand finish.
Miller drilled a fine drive just inside the post after taking a Campbell pass on the left edge of the area (80).
And then as Blues continued to press forward and a cross was headed clear towards the D, Stirk chested it down to his right to make space, cracked the ball on the volley and it absolutely flew past Richards (83).
Crewe looked for the long ball for Zanzala on the break as Blues strived to find another, and from one raid appealed for a penalty when he checked back on Geraldo Bajrami and went to ground, but the centre-half had just held his ground strongly.
Crewe thereon managed to protect their goal well enough to leave Blues frustrated and on the wrong end of the scoreline in a topsy-turvy encounter.
Blues: Clayton, Williams, Djurovic, Stirk, Bajrami, Redmond, Walker, Campbell, Hurst (Miller 74), George, Fernandez. Subs not used: Rouse, Andrews, Fogarty, Chang.