Erik Tonne scored the only goal of the game as the Blades U21s continued their strong start to the season.
Tonne's decisive strike early in the first-half means Chris Morgan's youngsters have won three of their four league matches to date, much to his delight:
"It was a good performance, nothing spectacular, but a good away performance and the lads showed good discipline to see the game out in the end.
"As you would expect against any Crewe team they had plenty of possession but we defended well and looked dangerous on the break.
"What was most encouraging was the performances of the young lads from the U18s, they all did very well and should take plenty of confidence from their performances."
The visitors scored the only goal of the game in the 17th minute, when Chapell beat two defenders before cutting the ball back from the byline for TONNE to sweep home for his second in as many matches.
Moments later it could have been two when Philliskirk was denied after Tonne had slid the striker through on goal.
The second-half saw the home side have the majority of the possession but marshaled by Chris Salt and Terry Kennedy, United's backline rarely looked unduly troubled and deservedly registered a clean sheet and three more points.
Blades: Willis, Hodder, McFadzean (Smith 74), Harriott, Salt, Kennedy, Chapell (De Girolamo 84), Pemberton, Tonne, Philliskirk, T. Williams.
Unused: Lynch, J. Williams, Whiteman.