Gary Ablett made five changes from the team that battled for a well-earned point against Southampton on Saturday.
Owain Fon Williams, Danny Pilkington, Greg Tansey and Peter Thompson were all rested whilst skipper Michael Raynes missed out after straining his hamstring against the Saints.
Nicholas Bignall was handed his County debut after arriving on loan from Reading yesterday; Lloyd Rigby, Liam Bridcutt, Andy Halls and Paul Turnbull also started.
The Alex included two former Hatters, goalkeeper Adam Legzdins and young defender Harry Worley; a third, striker Anthony Elding, was on the bench.
A second successive away hat trick from Carl Baker plus a debut goal from Nicholas Bignall saw County safely through to the Johnstone's Paint Trophy second round.
It was Crewe who made all the early running, though, until Baker struck on seven minutes. Michael Rose's inswinging corner was flapped at by Legzdins, under pressure from Bignall, and the ball broke kindly to Baker who smashed home a left-p0footer.
Alex were undeterred by the setback though and Bryan Moore was unlucky to see his shot deflected for Calvin Zola and bounce behind for a goal kick.
They cam even closer on 15 minutes when Worley's towering header bounced to safety of the angle of post and bar.
Crewe threatened again on 18 minutes when Moore played in Steven Shumaker who seemed to lose his footing when he was about to shoot and Rigby saved.
Rose relieved the pressure with an angled shot that forced Legzdins to save.
But Alex were soon back on the attack and Billy Jones brought a flying save out of Rigby from 25 yards.
The pressure continued with Zola and then Grant coming close before County hit them with another sucker-punch.
Legzdins, again under pressure from Bignall, failed to deal with another Rose corner and the ball again dropped to Baker who smashed home an identical shot with his left foot on 33 minutes.
Seven minutes later the Alex 'keeper tipped over a trademark Rose shot from distance.
Four minutes before the break the vociferous Blue & White Army, who had travelled across Cheshire in great numbers, were celebrating a third County goal; and what a goal it was.
Liam Bridcutt raking pass released Bignall who held off the challenge of Simon Walton, cut inside and finished superbly.
And, incredibly, a couple of minutes later it was almost 4-0. Bridcutt's audacious back heel released Rose who crossed from the left. Vincent, coming in a t the far post, saw his header saved.
Four minutes after the break Baker went hunting his third. A mazy run past three defenders ended with a chip that Legzdins saved.
Alex introduced Elding at the interval set himself up with a brilliant touch; fortunately he dragged his shot wide.
To their credit Crewe hadn't thrown in the towel and Rose had to be strong at the far post to stop Zola getting in a free header on the hour. A minute later the dangerous Joel Grant cut inside Andy Halls and hit a low drive towards the near post that brought a fine save out of b Rigby
Greg Tansey's first touch after coming off the bench was to set up Baker. His powerful drive from the right of the box beat Legzdins but hit the side net.
Crewe scored a consolation in the final minute. Rigby made a terrific save to deny Elding but Zola pounced to hammer home the rebound.
There was still time for Baker to go home with another match ball, though. Danny Pilkington brilliantly worked an opening down the later and pulled the ball back to the former Morecambe man who beat Legzdins to send the travelling hordes into raptures.



















