When the sides went in at the interval all square at 1-1, Crewe had worked themselves back into the game following Steve Foster's equaliser after Michael Ricketts had given City an early lead.
But after the interval City ran riot and Joe Ledley, Kevin Cooper, skipper Darren Purse from the spot, Cameron Jerome and Jason Koumas reduced the visitors defence to shreds.
City were unchanged for the third successive game while Wales international David Vaughan found himself on the bench for the Railwaymen.
The Bluebirds went ahead in the 18th minute with Ricketts netting his fourth goal since his loan move from Leeds. Two Crewe defenders collided going for the same ball and Ricketts ran through to fire a crisp drive into the net.
The visitors hit back against the run of play from a set-piece on the half-hour. Kenny Lunt swung a free-kick into the area and Foster was left unmarked to head over Neil Alexander and into the roof of the net.
It took only three minutes of the second half for the Bluebirds to regain the lead. Jerome swung a pass out wide to Ricketts and his deep cross was headed into the corner of the net by Ledley.
A double save by Alexander kept the Bluebirds ahead. Mark Rivers beat the offside trap but City's keeper spread himself to make the block. When the ball was fired back into the danger area Alexander dived to gather.
A piece of Koumas magic helped City go further ahead in the 59th minute. His delightful ball split the Crewe defence and Cooper raced in to side-foot past the advancing keeper for his first goal for the club.
Alan Lee had only been on the field four minutes when he won a penalty after being brought down in the area. Up stepped skipper Purse to hammer the spot-kick home.
Crewe were now in tatters and when Jeff Whitley slid a ball through to Jerome the youngster made no mistake, although he needed a slight deflection to beat Ben Williams in the visitors goal.
Still City weren't finished and Koumas added his name to the growing list of scorers in the 74th minute when he strode through the visitors defence before rifling his shot into the far corner.
The Bluebirds were now attacking from all areas but Crewe managed to baton down the hatches and prevent any further goals in the closing minutes.