Conor Sammon led the way to victory with his first goals in a Blades shirt.
The on-loan striker scored twice as the Blades secured a deserved victory at Peterborough United.
Jose Baxter completed the victory with a third goal late on, whilst Souleymane Coulibaly got the home side back into the game.
Boss Adkins named the same starting line-up after the 2-0 success over Chesterfield at the weekend. The bench was also unchanged.
The opening 25 minutes were eventful and included a goal and three injury substitutions! Freeman and Sammon saw early crosses cut out, whilst for the home side Bostwick fired wide.
Peterborough withdrew left-back Ntihe moments before United took the lead, with a well-worked move. A ball down the right channel saw Sharp hold up possession before laying into the path of SAMMON, whose shot was too hot for goalkeeper Alnwick.
The Blades, however, lost both Scougall and Collins to injury within the space of six minutes, which forced McEveley into a central defensive role in a reshape. Headers from set-pieces at both ends were off target, Santos for Peterborough and McEveley for United, whilst the visitors finished the half the stronger.
Freeman laid off to Sammon but his goalbound shot was blocked and then defender Edgar headed a Campbell-Ryce free-kick wide at the back post. Due to the injuries, there was six minutes of added time and final chance fell to the home side but after a couple of ricochets, Gormley was put off by the onrushing Howard.
Peterborough made the better start to the second period. Anderson beat Wallace and Basham but shot wide and Collison arrived late to volley Maddison's cross but Howard parried away. The home side introduced COULIBALY and he took just five minutes to make a difference. The substitute cut in from the left, held off Freeman and curled past Howard's left hand.
United hit back with three Sharp efforts, the first from Wallace's throw, the second from Campbell-Ryce's pass and the third from Basham's lay-off, but all failed to find the target as the final 20 minutes approached.
However, a second United goal was on the way as the pressure told. Adams was looking dangerous on the left and he turned down a shooting chance to lay off to SAMMON, who slotted home with his left foot from ten yards.
Adkins made his last chance with James Wallace taking over from Sharp but, understandably, the home side went on the offensive. Coulibaly's back post header was straight at Howard, Bostwick fired wide and Santos cleared the stand.
Peterborough's hopes of a comeback, however, were dashed on 85 minutes, with a third Blades goal. Substitute James Wallace's 50-yard burst ended him laying off to fellow Scouser BAXTER, who beat Alnwick with the aid of the underside of the crossbar.
In the closing stages, Coulibaly fired over but the home side knew they weren't getting back into the game, even when four minutes of added time was announced, as United completed back-to-back wins.
Posh: Alnwick, Nithe (Brisley 14), Zakuani, Bostwick, Maddison, Santos, Washington, Davey (Payne 73), Gormley (Coulibaly 54), H Anderson, Collison.
Unused: Henry, Taylor, Vassell, J Anderson.
Blades: Howard, Freeman, Basham, Sharp (J Wallace 75), Baxter, Collins (K Wallace 25), Scougall (Campbell-Ryce 19), Sammon, McEveley, Adams, Edgar.
Unused: McNulty, Woolford, Reed, Long.