Sheffield United started strong with Callum O’Hare dribbling into the box and his cut-back deflected off Bachmann to trickle over the line.
The home side had the chance to double their lead 10 minutes later when Arblaster was fouled in the box by Yasser Larouci, but Moore’s penalty was saved by Bachmann low down to his left.
Chris Wilder’s Blades felt they should have had a second penalty on the stroke of half-time when Moussa Sissoko tugged the ankle of O'Hare after he fell and tried to get back to his feet, but his pleas were ignored by referee Andrew Kitchen.
Ryan Andrews hit the post from distance in the second half and former Blade Daniel Jebbison came on for his Watford debut as the visitors searched for an equaliser.
But it was Kieffer Moore who missed the best chance of the second-half to seal the win 10 minutes from time, with his one-on-one effort kept out by Bachmann.
It was a nervy finish around Bramall Lane and it threatened to boil over at the end after some physical challenges, but Sheffield United held on for their first home league win since December 2023.