Both sides were winless heading into this tie, with a total of 18 games and no wins on the board.
But a first half strike from Chelsea loanee Conor Townsend proved the difference in the West Midlands as Slaven Bilic’s team edge out of the relegation zone.
The Blades were the brighter in the opening stages as Oli McBurnie and John Fleck both wasted early chances.
But with the visitors unable to find a cutting edge despite creating chances, West Brom took full advantage on 13 minutes.
Mateus Pereira’s corner was only cleared to the edge of the box and Gallagher was onto the loose ball in a flash and drilled past Aaron Ramsdale.
But Chris Wilder’s side were quick to react to that as Sam Johnstone produced a fantastic stop from Oli Burke.
It was the hosts that enjoyed the better chances just after the break as Ramsdale was called into action to deny Kyle Bartley and Callum Robinson.
That left the door open for the Blades late on but their familiar lack of cutting edge came back to haunt them again as West Brom hung in for that vital first win.
Full Time at The Hawthorns it’s West Brom 1 Sheffield United 0