In an action-packed game, United completed a first double of the season and also moved up to second in the table.
First half goals from Billy Sharp and Stefan Scougall set the Blades on the way to victory in a game that saw two red cards and missed penalty.
Boss Wilder named an unchanged team, the starting XI that extended the unbeaten run at Chesterfield were given the green light to face Shrewsbury. There were changes on the bench, Ramsdale and Chapman, back from international duty, took over from Long and Whiteman.
United quickly asserted themselves and put the Shrews on back foot. A good move down the right saw Duffy's effort inadvertently blocked by team-mate Freeman just moments before the home side grabbed the lead. A tremendous diagonal ball from Fleck saw SHARP beat the offside trap and then drill into the bottom corner, beyond Halstead's right hand.
Duffy limped off on ten minutes and Shrews hit back with a couple of half-chances but Deegan missed the target and Moore saved from Leitch-Smith following a mistake at the back.
But United were quickly back in the ascendency. Sharp shot wide and the home side had two penalty appeals turned down...but not the third! On 20 minutes, Lafferty latched on to a one-two with Done before falling under a challenge from O'Brien - referee Deadman waited but pointed to the spot and sent off the Shrews midfielder. However, after a delay, Sharp's penalty was pushed over the crossbar by Halstead.
A second Blades goal, though, was just a matter of minutes away. Coutts delivered a deep corner from the left, an unmarked Freeman headed back into the danger area and SCOUGALL poked home from close range.
Shrewsbury were under the cosh. Lancashire cut out a ball which would have put Sharp in the clear and two shots from Coutts were close. On 39 minutes, the Blades went mightily close again but El-Abd stopped the ball on the line following Scougall's effort after Lafferty had headed down a Sharp cross.
There was more drama before the half-time whistle. In injury-time, Ogogo became the second Shrews player to be shown a red card following a lunge at Coutts in midfield.
Coutts was obviously feeling the effects of the challenge as he did not re-appear for the second half - O'Connell was the replacement; Basham stepped into midfield and had an early header saved by Halstead.
Sharp had a shot saved and Done was crowded out by El-Abd as United continued to pour forward. However, on the hour, Freeman became the third Blade to leave the field injured and soon after Done picked up a knock, although he carried on, to keep up the two-man numerical advantage.
Scougall and Sharp failed to get enough on a Chapman cross on 67 minutes and Halstead was called upon to make routine saves from Chapman and Scougall.
The Blades were not making the most of their possession and territorial advantage and were stung in a rare Shrews attack. On 72 minutes, Ebanks-Blake won a throw and from a subsequent Brown cross, DODDS volleyed home.
United were quickly back on the attack. Chapman headed over a Sharp cross and Halstead made two impressive saves inside 60 seconds - firstly from Done, tipping around a post, and then Sharp's header from Fleck's cross.
On 87 minutes, a deflected Lafferty cross saw Sharp's back header beat Halstead but the ball struck a post, hit Brown and dribbled wide for a corner.
Three minutes of added time saw the Blades professionally keep possession and there was one more chance of note, Ebanks-Landell volleyed against Lancashire, before the final whistle signalled another victory.
Blades: Moore, Fleck, Basham, Sharp, Done, Wright, Coutts (O'Connell 45), Freeman (Chapman 60), Ebanks-Landell, Duffy (Scougall 10), Lafferty.
Unused: Lavery, Ramsdale, Brown, Clarke.
Shrews: Halstead, Lancashire, Ogogo, Toney (Black 45), Dodds, O'Brien, Brown, Grimmer, Deegan, Leitch-Smith (Ebanks-Blake 45), El-Abd.
Unused: Leutwiler, Sadler, Smith, Sarcevic, Waring.