Seven points from a possible nine indicate the Blades have turned the corner and it was a nice gesture to allow Chris Morgan, who had been in charge for the previous two games, to share the limelight with Clough before kick-off.
Clough’s reign began with a solid rather than spectacular victory, Maguire taking full advantage of slack marking to head home in the 19th and 30th minutes from a free-kick and then a corner from Stephen McGinn.
Ryan Flynn switched flanks and cut inside from the left to fire home inside Steve Phillips’s right-hand post after the break to make it game over at 3-0 in 55 minutes.
The only blot on the performance came when the Blades allowed Chuk Aneke to thread the ball through the middle for fellow substitute Max Clayton to prod the ball home in the 77th minute, causing some unnecessary anxiety among home supporters before seeing their club move out of the drop zone on goal difference.
Clough made just two changes to the side which drew at Peterborough in midweek, striker Marlon King replacing Fabien Brandy and Matt Hill returning at left-back as Simon Lappin moved into midfield and Conor Coady made way to the bench.
But former Derby manager Clough is already planning to bring in Leeds United left-back Aidy White on loan this week to strengthen the squad.
Maguire is convinced not many changes are required and has not ruled out a surge toward the play-offs. The central defender said: “We desperately needed the three points today. I’m delighted to have scored twice and it’s important we get a goal contribution throughout the side.
“You definitely want to get off to a good start under a new manager, I’ve already had a few in my career, but Morgs did a fantastic job when he took over (from the axed David Weir) and the gaffer has just followed on really, being really positive.
“I hope we can kick on from here. He hasn’t said a lot but is trying to give the lads a boost and it’s paid off.
“We have some momentum now to push up the table. The play-offs are definitely a possibility as it’s still early season.
“We had a poor start and knew we could have done a lot better but we have a strong squad with good ability and we now need to keep working hard.
“You have to be ruthless in both boxes when the chances come.
“We still have a lot to learn from the new manager but after what he did at Burton and then Derby I’m sure he’s going to have a big impact on the club.”
Clough, afforded a fine reception as he emerged in his Blades tracksuit top, admitted things could hardly have gone better.
“It’s been a great week and we have something to build on. We have things to work on, making things second nature for the players but there should be enough here to get us away from trouble.
“We can pass it a bit better at times and we got a bit nervy at times but that is understandable.
“Momentum is important – there is nothing worse than being in a dressing room where players are losing matches. Everybody gets low so they can be very proud of their week’s work.
“We just want them to relax and play.”
Clough was pleased with the emerging partnership between Lyle Taylor and the experienced King.
If anyone deserved a goal it was Taylor, not only for his non-stop harassing of the Crewe backline but for his ability to make space in the area and unleash a shot as he did in the 27th minute when he was only denied by the quick reactions of Phillips, flinging up his left arm to deflect the ball off target.
Of the 23-year-old, who scored 24 goals in 34 appearances for Falkirk before the Blades nipped in ahead of Rotherham to sign him on a two-year deal, Clough said: “He is a handful and puts himself about. It’s the first time we have seen him but he looked a bit shattered in the second half and needs to build some match fitness.”
Of his experienced partner and Jamaica international King, the new manager continued: “Marlon came in today and we are going to start with two up front as often as we can.
“He is still building his fitness and has not played really since February and it’s a big thing for a footballer missing pre-season.”
Both strikers were eventually withdrawn, Shaun Miller getting another chance to continue his comeback from cruciate knee ligament damage sustained on Boxing Day with a 69th-minute introduction against his former club as King ran out of steam.
Clough and his backroom staff, meanwhile, have clearly drawn a line under what happened under Weir and the manager explained: “We haven’t seen any of the games and purposely so. What happened in the first couple of months is largely irrelevant now. It’s what happens in the next 30-odd games that matters. We will judge everyone on face value.”
On Saturday’s evidence, Clough, employing a 4-4-2 formation, will have little tinkering to do, although sterner tests than the one presented by a youthful Crewe await.
George Ray took the blame as Maguire found himself free six yards out to produce a stooping header which put the Blades ahead and the central defender again lost his man as Maguire rose at the far post to make it 2-0.
George Long had tipped over an early header from Abdul Osman and Byron Moore volleyed off target before Flynn made it 3-0, goalkeeper Phillips being criticised by manager Steve Davis for not keeping out the shot from outside the area.
Aneke also volleyed against the bar shortly before setting up Crewe’s goal but threats from the visitors were few and far between as Maguire and Neill Collins bottled up the heart of the defence.
Sheffield United: Long, McMahon, Maguire, Collins, Hill; Flynn, McGinn, Doyle, Lappin (Cuvelier 90); Taylor (Coady 82), King (Miller 69). Unused substitutes: Howard, Westlake, Baxter, Murphy.
Crewe Alexandra: Phillips, Mellor, Ray, Dugdale, Tootle; Moore, Turton (Aneke 57), Osman, Grant, Inman (Clayton 74); Oliver. Unused substitutes: Ellis, Guthrie, Nolan, Garratt, Molyneux.
Referee: B Malone (Wiltshire).