Kembali
Phil Parkinson's side trailed at the break following a lacklustre first-half performance, with the mid-table Blades by far the better side.
But despite producing a better performance at the break, the Reds only had one attempt on target all game having previously also struggled to create decent chances in the 2-0 defeat at Blackburn Rovers in the previous outing.
Wrexham remain 17th in the table following the loss.
Parkinson made three changes from the side which started the defeat at Blackburn last Saturday.
Ben Sheaf, who returned from injury as a second half substitute at Bramall Lane, took over from Ben Whiteman in midfield.
With the Reds boss reverting back to a 3-4-2-1 formation after starting with two strikers in the previous two games, Ollie Rathbone and Lewis O'Brien came back into the side as number 10s to support lone frontman Kieffer Moore.
The duo replaced Callum O'Hare, who missed out on facing his former club through injury, and Sam Smith, while Max Cleworth and George Thomason were named on the substitutes bench after spells out injured.
The first chance fell to United as Romelie Donovan picked out Jordan Ayew who failed to hit the target from eight yards.
Donovan whipped in another cross from which Ben Brereton-Diaz headed wide as United continued to have the upper hand and there was another chance when the ball fell to Sydie Peck whose low drive was gathered by keeper Anthony Patterson.
There was a first Wrexham sight of goal when Matty James cut out a wayward pass and fed Jacques Ekomie whose cross was cleared to O'Brien and his goalbound effort was blocked by centre-back Japhet Tanganga.
However, United took the lead on the half-hour mark.
Wrexham were left open by Tanganga's pass to Ayew who saw his shot parried by Patterson but Brereton-Diaz was on hand to put away the loose ball.
United continued to press and Peck's effort deflected wide after the home side felt they should have been awarded a penalty following Dominic Hyam's tackle on Harrison Burrows.
Misplaced passes inviting pressure on themselves didn't help Wrexham's cause but they got to half-time without conceding another goal.
There was an opportunity for Wrexham early in the second half as Kieffer Moore raced onto James' ball over the top but he fired over.
It was an improvement with Wrexham getting out of their own half and stringing passes together as they began asking questions of United in the final third, with substitute Smith heading wide.
But the Reds needed a brilliant challenge by last-man Sheaf on Ayew in the area to deny the striker who raced onto keeper Michael Cooper's long clearance.
Patterson saved from Peck at the start of injury time while at the other end, Danny Imray couldn't keep his shot down after Thomason's cross came out to him.
Smith's late header was saved by Cooper and Wrexham suffered defeat.
Sheffield United (4-2-3-1): Cooper; Choudhury (McGuinness 86), Tanganga, Kitching, Burrows; Peck, Phillips; Chong (Seriki 68), Donovan (Campbell 86), Brereton-Diaz (Arblaster 79); Ayew (Cannon 68). Subs not used: Betts, McCallum, Rothwell, Riedewald.
Wrexham (3-4-2-1): Patterson; Hyam (Cleworth 46), Worrall, Doyle; Kabore (Imray 72), Sheaf (Dobson 72), James, Ekomie (Thomason 72); O'Brien, Rathbone (Smith 46); Moore. Subs not used: Ward, Vyner, Whiteman, Cadamarteri.
Attendance: 26,512.