The Blades recorded a victory and a clean sheet on a day when the 2015-16 home kit was launched and worn for the first time.
Jose Baxter scored the all-important goal, a first half penalty after Port Vale skipper Michael O'Connor fouled Jamie Murphy.
Jason Holt made his full home Blades debut and former favourite Michael Brown was sent off late on.
Howard captained the Blades as boss Clough made three changes. McEveley and Reed missed out through injury, whilst Doyle dropped to the bench. Basham returned after suspension to start, whilst Coutts and Steve Davies were recalled. Vale, managed by former United skipper Rob Page, included ex Blades Robertson and Brown.
United were the more positive early on, Harris fired over with a first time effort and a Baxter free-kick was deflected over. A challenge from Davies also put Vale goalkeeper Neal under pressure.
Brown was the first in the referee's book, he was punished for a 17th minute lunge on Freeman, and United's fine start continued. A great run and cross by Coutts saw Davies mis-kick and Murphy was causing problems for his marker, Yates.
Vale's two ex Blades combined to create their first chance of the game, on 22 minutes. A Brown free-kick saw Robertson win the header but Howard saved. United's goalkeeper also kept out a deflected effort from Brown before the home side opened the scoring.
Davies went close with a long-range shot from wide on the right minutes before referee Simpson spotted O'Connor's high tackle on Murphy in the box, immediately pointing to the penalty spot. BAXTER took responsibility for the spot-kick and drilled past Neal.
Blades fans - and stadium announcer Gary Sinclair - thought a second had been recorded three minutes later following another impressive move. Harris played a long, diagonal ball for Baxter to deliver into the box first time and Davies did the rest, but he was adjudged offside when he put the ball into the back of the net.
Coutts was booked for a cynical challenge on Moore and Basham was also shown a yellow card, ironically for a foul on Brown. Late in the half, Vale's final opportunity before the break saw Coutts make a timely challenge in the box.
Vale made a double substitution at the break and there was a lively start to the second period, with opportunities at both ends. Dodds and Done had half chances before a long-range shot from O'Connor was tipped over by Howard, who then had to be on his toes to keep out Marshall's near post corner. For United, from a quick free-kick, Coutts fired just wide.
The flow of chances dried up until 64 minutes when United almost added a second on the break. From Howard's throw, Murphy went on a mazy run but, following his pull-back, a shot from Davies was at Neal.
Flynn took over from Done and Vale completed their substitution quota on 68 minutes, whilst the crowd wanted Freeman to shoot when he found himself clear on the right, rather than trying to deliver into the box.
For the visitors, Veseli's overhead kick from the edge of the box was over and Daniel could not find the target when he was afforded the space to run at the Blades defence.
As the last ten minutes approached Doyle took over from Baxter. The game became frantic but Davies was impressive, he was involved in a move on 84 minutes which saw Flynn lay off and Murphy shoot but Neal gathered at the second attempt.
There was a nervous moment on 86 minutes when Howard slid out of the box when gathering the ball but he let go at the right time and then cleared.
The officials announced four added minutes but the later stages were not without incident. Davies almost converted a Coutts cross and ex Lane favourite Brown was sent off for a second bookable offence, catching Flynn from behind.
Alcock replaced the tiring Holt but United professionally saw out the final minutes to record a welcome victory in the first of three home games in the space of seven days.
Blades: Howard, Harris, Brayford, Basham, Murphy, Baxter (Doyle 80), Done (Flynn 66), Coutts, Freeman, S. Davies, Holt (Alcock 90).
Unused: McNulty, B. Davies, Turner, Adams.
Port Vale: Neal, Yates, Robertson, McGivern, Dodds (Campion 68), Williamson (Pope 45), O'Connor, Brown, Moore (Daniel 45), Marshall, Veseli.
Unused: Duffy, Birchall, Johnson, O'Sullivan.