Interim boss Chris Morgan guided the Blades to a second victory of the season at Bramall Lane on Saturday.
Micky Adams was the manager of Port Vale and he was responsible for signing both Neill Collins and Michael Doyle for United - the goalscorers.
Vale's goal was a freak effort from Adam Yates after Daniel Jones was sent off.
After impressing as substitutes last week, McGinn and Taylor were given opportunities to start and the third change made my interim boss Morgan was recalling McMahon after injury. There was a further boost to the Blades as Miller was named amongst the substitutes, his first senior appearance on the teamsheet since damaging his cruciate on Boxing Day last year.
United's early formation looked an orthodox 4-4-2 and the opening opportunities, three in the first ten minutes, were all from set-pieces. Taylor just failed to get on the end of a Collins head down, McMahon curled a free-kick into the arms of goalkeeper Neal from 30 yards and then Maguire headed a McGinn delivery just wide.
The set-pieces kept coming and it resulted in the Blades taking the lead.
McGinn was kicked in the head which resulted in a McMahon free-kick, which was deflected for a corner, which McGinn delivered and Maguire challenged for before COLLINS perfectly placed his header into the net, via a post.
Moments later Brandy curled over the top and both Maguire and Collins had runs out of defence before Vale created their first chance on 17 minutes. In a move in which referee Robinson played an advantage and later came back to book an unfortunate McGinn, who slipped as he made a tackle, Vale skipper Loft half-volleyed wide from the edge of the box.
The visiting side's first half problems continued. Jones was sent off for two bookable offences inside five minutes, the second a foul on Flynn. Additionally, Myrie Williams exchanged words with manager Adams as there was an early substitution and then Pope and Robertson were unhappy with each other.
A Maguire long-range effort caused problems for Neal and then a rare Vale attack saw Pope shoot wide after Hughes took the attentions of Collins.
The Blades continued to be the dominant force. Hill crossed from the left after linking with Flynn but Taylor's effort from inside the six-yard box was saved at point-blank range by Neal. Another chance close to the break saw Flynn pull back for Taylor but this time his effort took a number of deflections before rolling wide and then Collin shot at the goalkeeper following a corner.
It was undeniable that the Blades had bossed the first half and if you needed any confirmation that the home side's luck was out it arrived two minutes into four minutes of added time. YATES was only operating at left-back because of the sending off and after a quick free-kick his cross flew over the head over Long and in, off a post.
After the first half dominance, the Vale goal was a body blow but the Blades started the second half positively. Taylor's free-kick was just wide and a Flynn shot was saved by the visiting goalkeeper.
Doyle and McMahon fired over as United continued to push back the visitors and there was a huge cheer midway through the half when Miller was introduced for his first competitive game since Boxing Day 2012.
Hill cut in from the left and fired over with his right foot, whilst a Vale chance saw former Blades youngster Robertson head over a corner on 73 minutes.
Another Vale corner paved the way for the Blades retaking the lead a couple of minutes later. Long rolled out to Flynn to pave the way for the counter-attack and after the Scotsman exchanged passes with McMahon, he laid off for DOYLE, who took steadying touch before firing into the bottom corner
As the final ten minutes approached a McMahon effort was parried away by Neal, who did likewise to keep out Flynn a few moments later. Neal also denied Miller a comeback goal on 87 minutes as a result of Collins bringing the ball out of defence.
Westlake replaced Flynn late on and four minutes of added time was announced. Vale threw caution to the wind in injury-time but the Blades, who replaced Brandy with Coady, despite Long colliding with Dodds and Hill and Maguire having to clear. There was another late chance for the Blades on the break but Coady was denied Neal... no matter, the points were secured!
Blades: Long, Maguire, Hill, Flynn (Westlake 88), Doyle, Taylor, McGinn, Collins, King (Miller 68), Brandy (Coady 90), McMahon.
Unused: Howard, Cuvelier, Lappin, Murphy.
Port Vale: Neal, Yates, Jones, Robertson, Chilvers, Loft, Myrie Williams (Duffy 26), Pope, Lines, Griffith (Birchall 79), Hughes (Dodds 66).
Unused: Johnson, Shuker, Williamson, Mohamed.