The Liverpudlian, along with most of his Blades team-mates, struggled at the start of the League One season in a poor run of results which eventually cost Weir his job. Baxter only netted once under Weir, in defeat at neighbours Rotherham United.
But now the Blades midfielder has won over new manager Nigel Clough to earn a starting place and repaid the boss with goals on consecutive weekends.
He followed up his stunning goal in the FA Cup win at Cambridge United with a looping header which earned United all three points against promotion prospects Swindon Town.
“We played with two wide players and attempted to get them on the back foot,” said Clough. “The idea was to keep the pressure on and the goal finally came. Some may have thought the goal looked scrappy but it was a good header from Jose to loop it over the goalkeeper.
“We started well, lost our way a little at the end of the first half but then we were positive in the second half and deserved the win.
“Swindon have scored a lot of goals this season but we restricted them to long-range efforts and were positive in pockets, the aim now is sustain that.”
Swindon manager Mark Cooper had no complaints at the result.
“I feel a little frustrated but we can have no excuses,” Cooper said. “I’m disappointed but have no problems about the result.Sheffield United are a better team than their position in the table suggests.”
Sheffield United: Long, McMahon, Maguire, Collins, White (Hill 78), Flynn, Doyle, Coady, Murphy (Brandy 72), Baxter, Porter (Miller 85). Unused substitutes: Howard, Taylor, Cuvelier, Lappin.
Swindon: Foderingham, Nathan Thompson (Byrne 53), Hall, Ward, McEveley, Luongo, Mason, Kasim (Harley 70), Louis Thompson (N’Guessan 74), Pritchard, Ajose. Unused substitutes: Belford, Branco, El-Gabbas, Gladwin.
Referee: S Duncan (Tyne & Wear).
Man of the match: Jose Baxter.