United's youngsters were denied victory after two late goals - including one in the sixth minute of injury-time - earned Crewe a share of the points.
In a really open game from the start, United were on top in the first half and created the greater number of chances. Eastwood was forced to save after seven minutes when a long ball was not dealt with but this sprung the Blades into life.
Coustrain beat two players before shooting on goal, forcing a corner, Paling was wide with a rasping shot and Wright struck a post on 31 minutes. In addition, Reed's cross agonisingly avoided Cockerline and Coustrain, the latter proving a constant threat to the home side.
Before the break, Crewe went close but the Blades started on the front foot right from the kick off in the second half with Reed, Coustrain and Cockerline combining but Wright was unable to get on the end of the latter's cross.
A succession of corners followed before the Blades opened the scoring on 54 minutes. Good work on the left by Kelly ended with him pulling back for COUSTRAIN to slide home from eight yards out.
Heh replaced Partodikromo after the hour and he doubled the lead on 64 minutes. Quick play from Whiteman and Reed preceded HEH linking up with Wright before sliding the ball under the advancing goalkeeper from 12 yards.
Against the run of play Crewe were handed a lifeline on 80 minutes, a poor decision from Eastwood in possession gifted Crewe's striker a one-on-one and he took it to reduce the arrears.
In response, Cockerline's excellent header from Reed's corner was cleared off the line with the 'keeper stranded and then Crewe nearly equalised a minute later, Eastwood saved well through bodies and Cockerline himself then cleared off the line.
Crewe, though, equalised in the 96th minute after forcing three successive corners, from the last they headed home to complete their comeback.
Afterwards, Blades coach Travis Binnion commented: "It was a really strong performance for 80 minutes but ultimately we were undone by a lack of concentration and experience - for the second week running we haven't quite been able to hold on.
"The lads are unhappy with seven minutes added on. It was excessive, however, they need to see the game out and kill it off. Hopefully the nature of this result, on the back of last week's slip against Derby, will hammer home the importance of managing a lead."
Blades: Eastwood, Paling, Kelly, Reed, Whiteman, Cheeseman, Partodikromo (Heh 61), Ishmail, Cockerline, Wright (Smith 70), Coustrain (Brown 88).