United's Premier League Cup adventure comes to an end at the round of 32 stage, despite a spirited performance at Bramall Lane on Thursday evening.
In a typical Yorkshire derby on a cold night at S2, a well taken volley from Eoghan Stokes just before half-time settled the contest in the visitors favour, despite United battling gamely for a leveller throughout the second-half.
United started brightly under the Bramall Lane lights, Wright was proving to be a handful, Heh had a shot saved, whilst Brayford got forward at every available opportunity. At the other end, Walters appear to foul Banton before bursting into the box, but Whiteman blocked his attempted shot at goal.
The Blades continued to look the most likely to open the scoring and came close to doing so in the 20th minute, Dimaio broke up play, freed Heh, he ran purposefully at the visiting defence before freeing Coustrain who saw his shot saved at the second attempt by Peacock-Farrell.
With little under ten minutes remaining in the first period, the home side had the best chance of the game, but after neat footwork from Coustrain had enabled Whiteman to maraud forward and slot in the advancing Wright, United's number nine was denied well by the Whites goalkeeper.
Considering the Blades had enjoyed the majority of the game, it was somewhat against the run of play that Leeds took the lead in the 42nd minute. A long kick forward from Peacock-Farrell was flicked on by Doukara and having controlled the ball on his chest STOKES volleyed home from 25 yards, catching Ramsdale slightly out of position.
With the final kick of the half Stokes wasted a golden opportunity to double the visitors lead after a quickly taken free-kick had put Coyle in the clear down the right-wing.
The visitors made a double substitution before the restart with Parkin and Wilks replacing Bianchi and Doukara. Brayford bombed forward at one end, whilst Whiteman produced a timely intervention at the other in the opening exchanges of the second period.
United's first change saw McDonagh replace Heh on the hour, but the Blades were struggling to replicate the pressure they enjoyed in the first-half, as Leeds pressed for a second.
Coach Chris Morgan rotated his pack further with less than 20 minutes remaining, as Evans replaced Brooks, which saw Whiteman advance into midfield.
The final substitution saw Brayford receive a generous round of applause as he was replaced by youngster Gordon.
As the game entered the final minutes, the Blades had what appeared to be an excellent shout for a penalty waved away by referee Simms as Hamilton went down under a mistimed challenge from Skelton.
The chase for an equaliser was gathering pace and following a loose clearance from Skelton, only a last ditch challenge from Vann denied Gordon a route to goal. But ultimately United's efforts proved in vain as the exited the Premier League Cup.
Blades: Ramsdale, Brayford (Gordon 77), Phillips, Dimaio, Banton, Whiteman, Coustrain, Brooks (Evans 72), Wright, Heh (McDonagh 60), Hamilton.
Unused: Perryman, Cobain.