Midfield dynamo John Spicer proved to be the architect for Steve Cotterill's side with an energetic 90 minute performance.
Burnley were quickly out of the blocks with Spicer firing into the sidenetting after only four minutes. Leading scorer Ade Akinbiyi was denied by a fine save from Ben Williams and dangerous winger Nathan Dyer burst between two defenders before shooting wide as the home side dominated.
James O'Connor and then Garreth O'Connor twice went close before the deadlock was finally broken.
Burnley's early dominance was rewarded on 27 minutes with a fluent counter attacking goal from a Crewe corner.
Goalkeeper Brian Jensen started off the move as he fisted the ball clear to Garreth O'Connor, who found central defender Frank Sinclair galloping out of defence, before receiving a return pass and then launching a diagonal ball to Akinbiyi, who laid the ball off for Spicer to strike a first-time shot from 20 yards past Williams.
The home team had to reshuffle the centre of their defence when John McGreal had to leave the field following a clash of heads with fellow Claret Jon Harley and required nine stitches.
Crewe had a couple of opportunities to equalise at the start of the second half, but once Spicer had extended the lead with his second goal the result was never in any doubt.
Again this was a fine move involving Micah Hyde, Garreth O'Connor and then Spicer, who played a perfect one-two with Akinbiyi and found the corner of the net.
The scoring was completed just three minutes later as Spicer this time turned provider for Dyer to drive the ball home for his second goal since joining on loan from Southampton.