A late Marc McNulty goal secured United's place in the Capital One Cup second round.
He pounced with four minutes to go after Alex Fisher had cancelled out Andy Butler's goal in the Bramall Lane clash with League Two Mansfield Town.
Manager Clough made eight changes for the first round fixture. United's team included long-serving Doyle and Collins, whilst Butler, McNulty and Campbell-Ryce were given full debuts.
Baxter began from the left and Campbell-Ryce on the right as Porter partnered McNulty in attack - the latter came close to punching a hole in the Mansfield defence inside the first minute.
Moments later a crisp passing move through midfield saw Doyle put Baxter through but his shot was parried away by goalkeeper Studler, whilst deliveries from Davies found the central defensive pairing of Collins and Butler, but neither was able to break the deadlock.
Mansfield hit back with Heslop and Beevers linking up, the resulting cross from Clucas was cut out by Harris, and then Sutton's shot in a crowded penalty area was blocked. On 33 minutes a powerful run from Heslop paved the way for a Clucas shot but Howard dropped to his right to push the ball away.
The final ten minutes of the half saw the Blades in the ascendancy. Baxter's 35-yard effort was just wide, Davies curled a free-kick wide and yet another cross from Davies just evaded the dives of McGinn and Porter.
Early in the second half Heslop's long-range shot was deflected wide and from the resulting corner Clucas headed on to the top of the crossbar. United's first move after the break was similar but the result was different.
Doyle's 35-yard shot was deflected wide and from a Davies corner, Baxter's header was pushed away by the visiting goalkeeper into the path of BUTLER, who dived to head home at the back post.
The lead, however, lasted just four minutes. Beevers was involved before FISHER found the target, possibly with the aid of a deflection.
Further headers from Butler and Collins - both from Davies deliveries - came close to restoring United's lead, whilst Clough threw on Murphy and Higdon with around 20 minutes to go.
In the final 15 minutes, McNulty attempted to take advantage of a chest back to the goalkeeper by Beevers and another long-range effort from Doyle was saved by Studler.
The winner did arrive, though, on 86 minutes. Baxter and Higdon were both involved before McNULTY held off his marker and patiently waited to pick his shot, which was too sharp for goalkeeper Studler.
It was McNulty's last contribution, he was substituted for the more defensive-minded McGahey soon after, and the four minutes of added time were comfortably negotiated to ensure a first passage into the second round of the League Cup since 2011-12 season.
Blades: Howard, Harris, Butler, Doyle, Baxter, McNulty, McGinn (Murphy 71), Collins, Davies, Porter (Higdon 72), Campbell-Ryce.
Unused: Basham, Flynn, Willis, McGahey, De Girolamo.
Mansfield: Studler, Sutton, Riley (Dempster 72), Tafazolli, Fisher, Hearn (Clucas 15), McGuire (F. Bell 67), Heslop, Beevers, Taylor, Clements.
Unused: Jones, Thomas, Belford, A. Bell.