Carlisle United dominated long spells of the second half at Bramall Lane but they came away with nothing to show for a good display as the Blades made a good first half count with a goal from Jose Baxter.
Loanees James Pearson [Leicester] and Reece Brown [Watford] made their debuts for the club with Pearson, son of former United boss Nigel, making his first ever start in league football.
The Blades went on the attack right from the off when Jamie Murphy skipped past Pearson to get to the byline. He feinted to cross but dropped a shoulder and almost caught Pickford off guard when he drilled a shot at the far corner. The Carlisle stopper did well to spread himself and make the save.
Brown reacted first to head the outswinging corner away and Chimbonda stepped in to win the second ball when Flynn shaped to shoot.
More good work in midfield from the home side took Flynn into space and his back heel put Scougall through to the edge of the box. He had options left and right but he chose to shoot and his effort went right at the keeper.
A quick break down the Sheffield right took Byrne into a good area but a late sliding tackle prevented the cross from reaching Miller. Howard advanced quickly to punch the resulting corner out from beneath his bar.
The hosts looked confident and a direct pass from Doyle caused a brief moment of panic for Brown as he stretched to cut it out. It sliced off his shin but Pickford was alert and he scampered across to gather it up.
David Amoo looked up for the challenge and he worked space with Potts to deliver a wicked cross across the face of goal. Miller turned away in frustration as it skipped off the surface and away to safety.
Hesitation from Collins allowed Berrett to nick possession as the Blades tried to build from the back and Amoo called for it once more with space on his side. He went for glory from distance but the shot lacked conviction.
Sheffield pushed forward once more as the action ebbed and flowed and Coady fed Baxter with his back to goal. A drop of the shoulder gave him the space he needed but he scuffed his shot and dragged it well wide of the upright.
The Blades thought they'd grabbed the lead on 19 minutes when Scougall tussled for the ball in midfield. It broke kindly for him as Chimbonda slid in to stop the move and a quick exchange with Baxter left him one on one with Pickford. The Black Cats loanee earned a round of applause as he stood his ground to complete an excellent save.
Wide man Jamie Murphy saw plenty of the action and he fizzed another rasping cross into the box as he went through two challenges on the Carlisle right. Scougall and Baxter tried to connect but they couldn't find the touch they needed.
The home side were patient in the build up and a crisp run of passes left Flynn with a choice to make as he came in on the angle. He shot through legs and it whistled past the post with Pickford rooted to the spot.
It was impressive and decisive football which gave the Blades the lead as a powerful through ball from Coady was beautifully controlled by Baxter. His first touch gave him time to spin, move it a yard to the right and clip it past Pickford and into the back of the net via the base of the upright.
Carlisle tried to respond quickly from the restart but Potts miscued his shot from distance and Howard was able to watch it go wide.
Sam Byrne was next to have a go when he trapped the ball 30 yards from goal. He turned away from his man but was left to throw his arms in the air in disappointment as his shot disappeared off into the stands.
It was better from the Blues and Potts stepped in again to test the target. His shot with the outside of his right boot had Howard worried as he plucked it from beneath his bar.
A hurried throw from the Blades stopper heaped the pressure on his back line and David Amoo streaked clear to angle his way into the area. He had Miller and Byrne screaming for the cut back and the trio were left to turn away in frustration as Howard tipped the poked shot from out of the path of the advancing blue line.
The Blades picked up the pace of the game from the restart and Murphy danced past Chimbonda and Berrett as he made another arcing run down the right flank. He decided to go it alone but his shot, from a tight angle, was always heading behind.
Carlisle caused problems for themselves when Brown underhit a backpass for Scougall to chase but Pickford showed good feet to outwit his man and eventually hook the ball clear.
There was more for Pickford to do on 58 minutes when Murphy beat the offside trap to get to a lobbed ball over the top. It took him an age to get it under control and that allowed Pickford time to pounce to make another vital intervention.
A heavy tackle on Noble left him to limp from the field just after the hour and the reshuffle of the pack gave United some momentum as they started to push forward. Potts and Miller had shots blocked at source and a deep free kick from Berrett was plucked out of the air as Miller stood back to meet it.
Chris Chantler used the opportunity to get forward and his low cross deserved better as it beat everyone and raced away. Pearson sent it back into the mix and Potts was unlucky to see his deflected volley bend just wide. Dave Symington was next to have a go but his thunderbolt took another touch from a striped shirt and whipped past the woodwork. Berrett sent the corner to the penalty spot and it needed a man on the line to prevent an Amoo header from creeping in.
The Blades finally showed as an attacking force again late in the day with a free kick which had to be watched as it came into the area. Brown glanced it and Pearson completed the clearance as Porter tried to make it count.
Blades - Baxter (28)
Blades - Davies (48)
Sheffield United - Howard, Harris, Maguire, Flynn (Freeman 86), Doyle, Baxter (Porter 69), Collins, Coady, Scougall (McGinn 69), Davies, Murphy. Subs - Hill, Miller, Paynter, Long.
Carlisle United - Pickford, Pearson, Chimbonda, Brown, Chantler (Brough 90), Noble (Symington 63), Potts, Berrett, Amoo, Byrne (Novo 72), Miller. Subs - Fleming, Redmond, Guy, Meppen-Walter.
Referee - Mr Carl Boyeson
Attendance - 15,437 (238 away fans)