Two goals in the eight minutes at the end of the first half decided this encounter between two teams at the wrong end of the Sky Bet League One table.
Unfortunately, Chuks Aneke netted both as Crewe moved further away from the Blades. In injury-time substitute Byron Moore added a third.
In miserable conditions, the Blades failed to seriously trouble Alex goalkeeper Ben Garratt, suffering a third consecutive league defeat on the road.
Scougall made his first start in a Blades shirt as boss Clough opted for two changes, Paynter was also recalled. Porter dropped to the bench and Doyle started a three match ban. Harris, who completed a permanent move to United late on Friday night, was on the bench and joined by young midfielder Whitehouse.
It was soon clear that the biggest early threat would be posed by the swirling wind, although the rain had stopped in Cheshire at kick-off.
Hill cleared when Leitch-Smith looked in a dangerous position and the home fans were disappointed with a few early decisions - as were the Unitedites when Paynter looked to have been eased away from a cross as he went for a header in the box. The only half-chances of note for the visitors in the opening half hour both dropped to Scougall but his first effort was from distance and his second was blocked.
Crewe fired a couple of warning shots as they had a spell on top. Collins was forced to block from a Leitch-Smith shot and Long had to collect a Pogba cross from under the crossbar before the home side took the lead on 37 minutes. Just before the rain joined the wind in making conditions more difficult, ANEKE held off Coady and just before Maguire's tackle arrived, the striker curled into the bottom corner from the edge of the box.
Paynter prevented Davis from seeing the ball out as the Blades looked to hit back but the striker's cross for Baxter was cut out and on the stroke of half-time the visitors were hit by another blow.
Despite one of his assistants being ten yards away and not indicating a foul, referee Sarginson penalised Hill for obstruction and from Leitch-Smith's free-kick, the Blades could only clear as far as the edge of the box and ANEKE drilled into the opposite corner from where he scored his first.
There was a renewed vigour about United at the start of the second half and Crewe were planted on the back foot. Scougall thought he had been fouled in the box when he was about to shoot moments after the restart and then Coady almost turned in Baxter's cross on 50 minutes.
Crewe remained a threat, though. From a Tootle run, Leitch-Smith's shot was blocked by Brayford after Aneke rounded Long and Pogba turned Inman's cross just around the post.
With the initial second half onslaught not heralding a goal, boss Clough made a double change on 62 minutes with Harris and McGinn taking over from Murphy and Flynn - the changes also saw the Blades switch to three at the back. As United adapted, Pogba's effort was smothered by Long and Inman curled wide before Clough used his last change, Porter replacing Paynter.
Porter had two quick opportunities to make an impact, however, he was unable to get on the end of a Harris cross from the left, whilst from a Brayford delivery he headed wide on 74 minutes.
Aneke cleared from under his own crossbar as Crewe were again put on the back foot late on - another corner saw Maguire head wide. However, the remaining minutes, plus an extra four for injury-time, could not produce a goal and deep into injury-time, the home side added a third - MOORE turning the ball home after Long parried Inman's shot.
Crewe: Garratt, Tootle, Davis, Ellis, Pogba (Ikpeazu 87), Leitch-Smith (Moore 76), Inman, Guthrie, Evans, Aneke, Grant.
Unused: Phillips, Mellor, Dugdale, Osman, Water.
Blades: Long, Brayford, Maguire, Hill, Flynn (McGinn 62), Baxter, Collins, Coady, Paynter (Porter 68), Scougall, Murphy (Harris 62).
Unused: Howard, Miller, Whitehouse, Kennedy.