World champion boxer Kell Brook was guest of honour at his home-town club and saw Jose Baxter deliver the knockout blow at Bramall Lane.
Baxter’s first-half penalty helped the Blades end a run of five games without a win to remain fifth, two points clear of Peterborough, who moved ahead of Barnsley.
The penalty came when Michael O’Connor fouled Jamie Murphy midway through the opening half.
Former Blade Michael Brown was also sent off in stoppage time for a second yellow card. He was booked in the 17th minute for a foul on Kieron Freeman and then for a second time for a challenge on Ryan Flynn.
Sheffield United manager Nigel Clough said: “It wasn’t a brilliant game, but it’s a good clean sheet and probably the most important three points we have won this season. I thought we started well. We got the goal, then they got back in to it, and the defence dealt with how direct they played. We probably should have scored more, but we will take the win.”
The Blades made a bright start only for Matt Done to be crowded out. Steven Davies, the striker on loan from Blackpool, also troubled Vale throughout and was denied a goal by an offside flag while Murphy was also back to his best.
The action became somewhat ragged after the break and the Blades were fortunate when Mark Howard slid out of his area clutching the ball but none of the officials spotted it.
Sheffield United: Howard, Freeman, Brayford, Basham, Harris, Done (Flynn 66), Coutts, Holt (Alcock 90), Murphy, Baxter (Doyle 80), Steven Davies. Unused substitutes: McNulty, Ben Davies, Turner, Adams.
Port Vale: Neal, Yates, Robertson, Veseli, McGivern, Moore (Daniel 46), Brown, O’Connor, Marshall, Dodds (Campion 68), Williamson (Pope 46). Unused substitutes: Duffy, Birchall, Johnson, O’Sullivan.
Referee: J Simpson (Lancashire).
Man of the match: Steven Davies.