Matt Done's second-half goal proved enough to be enough as the Blades progressed to the third round of the Emirates FA Cup with a hard fought win over Oldham Athletic at Bramall Lane.
Done's strike in the opening minutes of the second period means United are safely in the hat for Monday's draw which sees teams from the Championship and top-flight enter the fray, despite finishing the game with ten men following a red card for Che Adams.
For Saturday's third round clash against the Latics, boss Adkins made two changes from the starting XI which drew at Barnsley, with Adams and McEveley replacing the injured duo of Campbell-Ryce and Edgar.
Inside the opening minute, United came close to opening the scoring. Brian Wilson got in a tangle on the edge of the box and after Cornell saved Done's initial shot, James Wilson blocked Adams's goal bound effort on the rebound.
At the other end, Oldham came even closer to breaking the deadlock in the 14th minute. After Hammond had fouled Winchester on the right-wing, Philliskirk hit the post from Brian Wilson's low set-piece.
In blustery conditions both sides found it difficult to find any real momentum, although for the Blades, Adams and Done looked a live threat. Meanwhile, Long was commanding when called upon.
Before the break, United survived a scare. Jones's corner from the right saw Philliskirk challenge Long and from the clearance a number of Blades bodies threw themselves in the way of Yeates's volley.
With the first-half drawing to a close, Harris required lengthy treatment following a clash from the aforementioned corner and in the end was stretched from the field of play. Four minutes added time were signalled as Kieran Wallace took the place of Harris at left-back.
United made a second change at the break with Scougall replacing Sharp, as Oldham got the second-half underway with the home side attacking the Kop end.
And inside two minutes United were in front. Collins advanced forward before feeding DONE, who twisted and turned before getting the better of James Wilson and slotting past the outstretched leg of Cornell.
On the hour Oldham had their first opportunity of the second period. A hopeful ball in from the right by Kelly wasn't claimed by Long, but the United goalkeeper made amends blocking Jones on the follow up.
With 25 minutes remaining, United were reduced to ten men as referee Ilderton brandished a straight red card to Adams following a clash with Oldham skipper Kelly. And the visitors wasted an instant chance to restore parity as Winchester headed over from a free-kick from the right.
United were now on the back foot and Cassidy should have scored in the 75th minute, heading over from Mills's left-wing cross with the goal at his mercy.
Sammon replaced Done with five minutes remaining, before Brayford came within a whisker of a goal, hitting the underside of the crossbar with a dipping left footed volley. At the other end, Long was United's saviour, coming quickly off his line to deny the advancing Poleon.
As four minutes added time were signalled. Hammond produced a timely intervention, before Long punched clear under heavy pressure on his line. Oldham's last effort saw James Wilson fire over from long-range as United held on for a place in the third round.
Blades: Long, Harris (K. Wallace 45), Brayford, Basham, Coutts, Sharp (Scougall HT), Done (Sammon 85), Collins, McEveley, Adams, Hammond.
Unused: Howard, Flynn, Reed, McGahey.
Oldham: Cornell, Mills, Dieng, J. Wilson, Kelly, Jones, Philliskirk (Poleon 71), Cassidy, Winchester, B. Wilson, Yeates (Rasulo 76).
Unused: Coleman, Vassell, Eckersley, Edmundson, Tuohy.