United made it three consecutive Sky Bet League One victories thanks to two second half goals.
Blackpool were resolute in the first half but Billy Sharp's first since returning and another from Marc McNulty maintained Nigel Adkins' unbeaten home start.
Adkins was forced into two changes following the midweek success over Peterborough. Collins (calf) and Scougall (ankle) missed out through injury so Kieran Wallace and Campbell-Ryce both recorded their first league starts of the campaign and it was quickly apparent that skipper McEveley had shifted back into a central defensive role.
United had plenty of early possession but the Blackpool back four were untroubled and goalkeeper Letheren did not touch the ball in the opening ten minutes. The visitors won the game's first corner and registered first serious shot, although off target, which was a 19th-minute 40-yard half-volley from McAlister and worried Howard enough into a full-length dive.
Basham headed over a corner and Sammon could not generate power on a shot on the turn, whilst from a free-kick Robertson headed straight at Howard on 34 minutes.
The best and last chance of the half arrived on 42 minutes and came from United. Baxter's weighted pass put Wallace around the back of the defence and from his pull-back, Sammon's side-foot effort was on target until being deflected just over the crossbar.
There was a scare for the Blades early in the second half. Basham was booked for foul on Potts and from the resulting free-kick, Ferguson curled against Howard's left post.
On 54 minutes Freeman played through to Adams but instead of shooting he laid off to Sharp, who was crowded out and soon after there was another golden opportunity. Campbell-Ryce beat three on the right flank and his low cross found Sammon, unmarked in the middle of the goal, but he could only direct the ball wide from inside the six-yard box.
Chief Adkins made a double change before the hour and the opening goal soon after. McEverley delivered a low corner, Basham made space in the box and SHARP's shot squirmed under the body of goalkeeper Letheren.
McEveley made an important block from Potts as Blackpool looked for a leveller before another of the home substitutes made an impact on 72 minutes. A ball down the left channel saw Sharp lay inside for McNULTY to take a steadying touch before drilling into the bottom corner of Letheren's net, at the Kop end.
Woolford tried his luck from range but Letheren gathered at the second attempt as the encounter entered the final 15 minutes, whilst a run from McEveley almost made a chance for McNulty.
In the last five minutes, Howard turned a long-range Potts shot around a post as Blackpool looked for a route back into the contest but the Blades stayed in control for the remaining minutes - plus four added - to register three more valuable points.
Blades: Howard, Freeman, Basham, Sharp, Baxter, Sammon (McNulty 56), McEveley, Campbell-Ryce (J Wallace 70), Adams (Woolford 56), K Wallace, Edgar.
Unused: Reed, Higdon, Long, McFadzean.
Blackpool: Letheren, Ferguson, McAlister, Robertson, Potts, Cullen (Thomas 79), Cameron (Redshaw 68), Oliver (Cubero 79), Aldred, Boyce, Osayi-Samuel.
Unused: Jones, Boney, Dunne, Higham.