A Billy Sharp hat-trick helped United down near-neighbours Chesterfield at the Proact Stadium.
The Blades' pre-season preparations continued with a win in Derbyshire, as Sharp took the headlines following goals either side of the interval, whilst new signings Callum Robinson and Luke Freeman were also on target as United enjoyed a comfortable win in sultry conditions.
Chris Wilder gave starts to three close season signings in Robinson, Luke Freeman and Phil Jagielka, and it was the former who created United's first opportunity.
After the Blades swarmed all over the Chesterfield penalty area during the opening minutes, Robinson eventually tried his luck with a 20-yard daisy cutter which struck the outside of Luke Coddington's right-hand post.
United were playing with speed and verve despite the unusual tropical environment, and after the hosts were slow to close down youngster Regan Slater, his deflected strike flashed narrowly wide of the far stick.
Robinson proved to be the scourge of the Spireites again on 13 minutes as he broke clear after winning a 50/50, but when about to take aim from the angle, defender Will Evans sprinted back to make a last-ditch challenge.
The one-way traffic continued through to the first break for drinks as Luke Freeman saw a rasping drive blocked from just inside the area.
Just before the half-hour mark, United won back possession high up the pitch, and it was Robinson again showing a keen eye for goal after his snapshot from distance was parried clear by Coddington.
On 33 minutes the pressure finally paid off. It was Luke Freeman who supplied the ammunition with a pinpoint left-wing cross, and SHARP rose to head beyond Coddington from eight yards out in front of the home faithful.
Sharp was denied a second soon after following more good work down the left. This time it was Enda Stevens who provided the cross but Sharp's effort at the back post was kept out by Coddington.
The shots continued to rain in before the break. After Coddington pushed a low cross into the path of John Lundstram, the midfielder steadied himself before sailing a well-hit strike wide as the 'keeper scurried back to dive full length across his goal.
The home side fashioned their first chance on the stroke of half-time as Evans' header was pushed behind by youngster Marcus Dewhurst who provided an assured performance between the sticks.
Four minutes into the second half it was 2-0. Slater rolled an accurate pass wide to Keiron Freeman and his low centre was turned in by ROBINSON leaving sub 'keeper Shwan Jalal with no chance.
The same player was somehow denied a second when after being put through on goal his strike deflected off the 'keeper onto the crossbar, with Robinson's headed rebound diverted wide by a sea of blue shirts.
Robinson seemed destined for more goals after another long-range effort was parried by Jalal.
On 62 minutes a barnstorming break from Luke Freeman created an opening for SHARP who cheekily clipped the ball over the onrushing Jalal for his second of the night.
With just under 15 minutes remaining the clinical SHARP completed his hat-trick. An accurate cross again from Stevens saw Sharp lurking at the back post, and another powerful header was too good for Jalal as United notched a fourth.
United rounded off the scoring in the final minute as David McGoldrick's effort was parried by Jalal, allowing Luke Freeman an easy finish in front of the travelling Blades.
Chesterfield: Coddington, Buchanan, Yarney, Evans, Maguire, Spyrou, Mandeville, Weir, Gerrard, Boden, Hollis.
Subs: Jalal, Rowley, Weston, Wedgbury, McKay, Wakefield, Smith, Sharman, Sheridan.
Blades: Dewhurst, Stevens (Fleck 77), Basham, Lundstram, L. Freeman, Sharp (Boyes 79), Robinson (McGoldrick 65), Jagielka (Stearman 77), K. Freeman (Baldock 67), Bryan, Slater (Norwood 67).
Unused: Moore, O'Connell, Egan, Brunt.
Attendance: 6,270 (3,365)