Three impressive first half goals paved the way for United's victory - and a 10th place finish in the Sky Bet Championship.
Leon Clarke, Billy Sharp and Kieron Freeman scored the goals to put the Blades 3-0 up at the break.
City, expectedly, hit back in the second half but United held on to finish the campaign with a victory.
Moore and Leonard started at Bristol City on Sunday lunchtime. Duffy dropped to the bench and loanees Blackman and Wilson returned to their respective clubs early, Chris Wilder revealed.
It was hot and bright at kick-off and the Blades were certainly the quicker into their stride. Home goalkeeper Fielding had to claw away an early Leonard corner before he was pulling the ball out of the back of the net. Just eight minutes had gone when CLARKE picked up the ball 25 yards out and curled beyond Fielding's left-arm. It was his 19th of the campaign.
United were clearly the front foot team without overly testing Fielding and the home side's only chance of the opening half hour saw the ball drop over Basham for Reid but Moore was quickly off his line to deal with the danger.
City's attacking momentum was stifled, somewhat, by having to defend. The home back line could do little about two volleys inside five minutes, though, that trebled the lead.
Firstly, on 29 minutes, Fleck teased a number of red shirts before dropping a pass over Kelly's head for SHARP to hammer past Fielding, into the roof of the net.
The third goal, however, was arguably better. Clarke's deep cross saw Fielding caught in two minds to collect or stay at home and that allowed FREEMAN to arrive at the back post and slam first time into the corner of the net.
Before the break Paterson headed over Bryan's cross and Reid volleyed wide, but the home side were still trying to contain the Blades. Clarke charged down Kelly's clearance but Flint blocked the subsequent shot and Evans curled over the crossbar.
Unsurprisingly, the home side began the second half with vigour but clear chances did not materialise until the hour when FLINT's header from a corner beat a number of bodies, including Moore, to nestle in the net.
It gave the home side momentum and they attempted to pepper the Blades box at every opportunity with set-pieces and Magnusson's long throw.
A second City goal arrived on 75 minutes following a Stearman foul. BRYAN's left-foot curler
beat the wall and found the top corner.
A minute later Diedhiou flicked on and Reid's shot was turned away by Moore whilst towering defender Flint was added to the City front line at every opportunity late on.
In the final ten minutes, the only chance of note saw substitute Brooks just fail to get on the end of Clarke's low cross, whilst five minutes of added time saw Moore twice leave his line to relieve his defence of pressure.
The final whistle confirmed the Blades had won on the first and last days of the return to the Championship, whilst the excitement in between resulted in a respectable finish.
Bristol City: Fielding, Bryan, Flint, Smith, Brownhill, Diedhiou, Reid, Eliasson (O'Dowda 56), Paterson (Magnusson 45), Pack, Kelly (Semenyo 79).
Unused: Taylor, Walsh, Steele, Bakinson.
Blades: Moore, Stevens, Fleck, O'Connell, Basham, Clarke, Sharp (Brooks 79), Leonard (Lundstram 58), Freeman (Baldock 63), Stearman, L. Evans.
Unused: Duffy, Lafferty, Eastwood, C. Evans.