The Clarets were knocked off top spot in the U18 Professional Development League as their six-match unbeaten run came to an end.
Burnley's last defeat in the competition had been a 5-1 loss at Crewe at the start of November.
And the young Railwaymen delivered another surprise result at the Barnfield training centre to lift themselves off the foot of the table.
The Clarets made a bright start, but Crewe snatched the lead midway through the first half and doubled it from the penalty spot soon after.
Craig Ellison (above) halved the deficit before half time to renew hope of a fightback, poking home on the rebound after Lewis King’s header rebounded back off the post.
And the Clarets came close to levelling it up after the re-start, with Mike Fowler, on for Marley Blair, going close with two headers.
However, as Burnley went for broke in the closing stages, and send goalkeeper Adam Bruce up for a late corner, Crewe broke to seal the victory with a third goal.
Assistant coach John Townson said: “We had a real good go in the second half but again, for the third week running now, we’ve had to come from behind.
“You can’t fault the lads’ efforts today but we lacked the killer touch in the final third and that ends a good run, but we’ll get back at it this week and prepare for the weekend.”
The Clarets, who travel to Leeds United next Saturday, slipped to third place in the northern division on goal difference following the defeat.