The Blades started well before Nicolas Pepe missed a golden chance for Arsenal after a slick counter-attack.
United went ahead on 30 minutes when Jack O'Connell's far-post header from a corner was turned in by the unmarked Mousset from close range.
John Fleck hammered a shot into the side netting after the break before Pepe had a free-kick saved.
Alexandre Lacazette and Gabriel Martinelli came off the bench as Arsenal searched for an equaliser but could not find a way past the joint-best defence in the league.
Sheffield United climb to ninth, on 12 points, while Arsenal drop to fifth on 15.
Sheff Utd: 26 Oct v West Ham (A)
Arsenal: 27 Oct v Crystal Palace (H)