The first away trip of the 2021/22 campaign took United to Bramall Lane to face the top-seeded side in round one of this season's Carabao Cup competition.
The team had a real Cumbrian feel to it with Lewis Bell and Josh Dixon making their first starts for the club, and with Taylor Charters also amongst the midfield ranks.
Keeper Lukas Jensen, on-loan from Burnley for the season, made his debut, with Manny Mampala another to get his first starting nod.
United won an early corner when a throw from Tanner was put behind to safety. Guy whipped it in but Verrips gathered comfortably as it was nodded high.
But there was a great chance for the Blades when a ball through the back line brought Sharp into the equation. He took a touch, but Jensen was out smartly to make an excellent block.
More work came for the keeper from the corner when Lopata got on the end of the outswinger. A thundering header was going in until the rooted stopper got his hands in the way.
It was a good spell for the home side and Freeman dropped a shoulder to put a ball at the near post from out wide. Smith moved off his marker but the close-range header was wayward.
The Blues were on the move in response when Bell robbed possession on the halfway line. Dixon took over, and he slid a pass through for Toure to overlap. He checked back as he reached the edge of the box and Basham rolled across at pace to make the tackle.
Trickery from Bogle earned a free kick tight by the corner flag and Freeman's pinpoint delivery was put behind for a corner by some attentive defending. Lopata was on the end of that one but he couldn't keep his connection down.
The big former-Brighton defender was a constant threat and he was forward for a free kick from deep when Brewster was felled by Feeney. He nodded it across the face of goal but Sharp lost his footing and could only watch as it bounced agonisingly past him, when all it needed was a touch.
A measured attack was sparked by the Blues when Guy showed good strength in his own half to win the ball back from Freeman. Charters and Toure pounced, with the former setting off on a run. It eventually came back to Toure, who dropped a shoulder, but his 19-yard effort was blocked.
United were undone on 24 minutes when Sharp beat the offside trap once again to get on the end of a ball over the top. A fierce 16-yard volley was parried by Jensen but he could do nothing as the Blades club record signing Rhian Brewster followed up to smash it into the waiting net.
Carlisle were almost back on terms on 32 minutes when Dixon was upended 30-yards out. Guy ripped a beauty of a free kick towards the back stick but Feeney looked on in desperation as it skipped just in front of his toe when he shook off his marker.
Good anticipation from Feeney in his own box prevented a tap-in for Sharp when he scampered quickly to cut out a cross from Freeman late in the half.
Guy let one fly at the other end, as the tempo of the game stayed high, but it clipped Lopata and bent away from the nets.
And Brewster had the same outcome for the Blades when a messy piece of play ended up with an unexpected opening. His effort came off Dixon and dipped over the bar.
United were a whisker away on 49 minutes when Mampala contested a miscued clearance from Basham. It was dinked towards Toure and a flick off the outside of his right boot edged just past the upright.
The Cumbrians were close again when a breakout was masterminded by Guy when he stole across in front of his own area. He had the ball at his feet, and Bell showed for it inside his own half. A powerful run was followed by a crunching pass which Mampala took in his stride. He feinted, then shot, but Verrips dived low to parry it.
Sheffield showed as a force moments later when Smith rode a challenge in the centre circle, with Brewster in close attendance. The pass forced the front man out wide and he blazed a poor attempt over the bar.
There were loud appeals for at least a free kick from the visiting contingent when Dixon was dumped to the ground on the 18-yard line, but the referee waved the shouts away after a short period of reflection.
A move which saw the ball go from right to left and back again gave Bogle an opportunity to deliver for the hosts. He found a good angle but it skipped up and McBurnie could only head it into the side netting.
Riley was needed to clear at the far post when Bogle popped a looped pass towards Lopata, and Jensen dealt with the recovery as Bogle once again tried to find a striped shirt.
Substitute Brennan Dickenson impressed the away fans with neat chest control from a raking Feeney pass just after he'd come on, and the cross that followed had Basham worried when it screwed off his toe. Verrips helped out with calm hands.
Chances dried up as the ball stayed in midfield but Mampala had a go when he wriggled into space after Abrahams had flicked it on. It lacked power and the keeper was well placed to cope.
An underhit back pass from Bogle had Abrahams really interested with 10 minutes left to play but his attempt at a drag back allowed Basham to clean up the mess.
There was a superb opening for Mampala moments later when a huge throw from Riley pinged around inside the box. The big forward stepped back and hit it at full throttle but it whistled just over the target.
And the Cumbrians thought they were going to be rewarded for their efforts when Dickenson beat his man with just one minute left to play. Abrahams timed his run expertly, but his header on the jump came off his shoulder and sped an inch too high.
The Blue Army behind the goal were willing the ball to go in when Toure was tugged by Norrington-Davies in time added on. Dickenson looked to find the sweet spot with the free kick but it had too much on it and the moment was gone.
Sheffield United - Brewster (24)
Sheffield United - Jebbison (90), Norrington-Davies (90)
Carlisle United - Armer (77)
Sheffield United - Verrips, Basham, Brewster, Sharp (c) (McBurnie 46), Freeman, Bogle, Brunt, Smith (Jebbison 65), Norrington-Davies, Gordon (Norwood 65), Lopata. Subs - Baldock, Lowe, Foderingham, Osborn.
Carlisle United - Jensen, Tanner, Feeney, Armer, Dixon (Dickenson 63), Riley, Guy (c), Bell (Abrahams 72), Charters (Mellish 63), Toure, Mampala. Subs - Norman (gk), McDonald, Alessandra, Whelan.
Referee - James Oldham
Assistant Referee - Daniel Woodward
Assistant Referee - Anthony Da Costa
Fourth Official - Andrew Kitchen
Observer - Gary Kellett
Attendance - 6,778 (524 away fans)