United's battling display went unrewarded as a goal in each half from Neil Warnock's well-organised Cardiff side earned them the points.
Goals from Sean Morrison and Nathaniel Mendez-Laing were enough for the early Sky Bet Championship leaders.
United named an unchanged squad for the encounter in south Wales. Despite Saturday's defeat, Wilder kept faith with the starting XI and substitutes.
It was the defence who were quickly forced into action as Cardiff started strongly, with a number of set-pieces and probes through the middle. Gunnarsson slung in three long throws in the opening ten minutes, whilst the home side won two corners and Basham had to be alert as Tomlin looked to close in on goal.
Tomlin sidefooted just wide after a patient build-up and Morrison's lay off, whilst on 19 minutes Hoilett cut in from the left and forced Blackman to acrobatically push around a post.
Three bookings in four minutes included Basham whilst home defender Richards let fly with a 30-yarder which rattled the crossbar on 25 minutes.
United's first chance arrived soon after. From Freeman's cross, Manga appeared to handle but Sharp played on and shot into the side-netting from close range.
Another Tomlin snap-shot went close before Cardiff put more pressure on the Blades goal. A low pass from midfield saw Zohore outpace Stearman before shooting through Blackman and just wide. To be fair to Stearman, he pulled up injured before play could restart and after a short assessment he was replaced by Wright.
A Fleck shot was blocked after Sharp caused problems from a clearance but one more attack and set-piece before the break saw Cardiff grab the lead. Mendez-Laing's pace helped win a corner and from a deep Ralls delivery, MORRISON rose highest to head home at the back post.
There was a quick opportunity for United to level before the break. The ball was shifted from left to right where Freeman whipped in a cross and Sharp volleyed on the turn, goalkeeper Etheridge looked stranded but the ball drifted just wide.
Further defending was necessary at the start of the second half. From a neat Ralls pass, Zohore's shot was saved by Blackman and Tomlin fired the rebound wide; then Basham was robbed by Hoilett and following a break, Zohore's near post effort brushed the side-netting.
There was a little respite as Coutts made space for himself to shoot from 25-yards but Etheridge was behind the ball and Cardiff returned to the attack to double their lead. A crossfield ball saw MENDEZ-LAING shake off Basham and fire across Blackman into the far corner of the net.
The pressure continued. From Gunnarsson's cross, Morrison's header was clawed away by Blackman, who moments later flew across his goal to tip Zohore's free-kick around a post.
Evans replaced Carruthers as the Blades searched for a way back into the game. Fleck's shot appeared goalbound but was blocked and Clarke was crowded out as he chased Sharp's ball over the defence.
Brooks replaced Stevens, indicating a change in system, and the young midfielder was soon in the thick of the action, he forced Etheridge to tip over an effort from the left. The resulting corner saw Clarke head over.
The final 15 minutes saw the game open up more and the Blades had plenty of the ball around the Cardiff penalty area but were unable to breakthrough. Brooks got ample touches and a Fleck ball towards the near post saw Etheridge gather as Sharp and Clarke looked to pounce.
In three minutes of injury-time, home goalkeeper Etheridge made two saves as United continued to push forward. He tipped over an Evans shot on the turn and from the resulting corner, a Fleck shot from the edge of the box was pushed away.
Soon after, the referee's final whistle indicated a long-trip back for 1,385 travelling fans, but only after the United players showed their appreciation.
Cardiff: Etheridge, Morrison, Ecuele Manga, Richards, Tomlin (Damour 68), Ralls, Zohore (Halford 88), Bamba, Gunnarsson, Mendez-Laing, Hoilett (Ward 79).
Unused: Peltier, Pilkington, Kennedy, Murphy.
Blades: Blackman, Stevens (Brooks 73), Fleck, O'Connell, Basham, Clarke, Sharp, Coutts, Freeman, Stearman (Wright 35), Carruthers (Evans 63).
Unused: Lundstram, Duffy, Lafferty, Eastwood.