Tony Pulis's side, which drew 2-2 at Millwall in their season opener, started brightly against the Blades and took the lead just seven minutes into the match.
Wing was also instrumental in Boro's second on 18 minutes as his corner fell kindly to Aden Flint, who rose above the Blades back line to nod in his first goal for the club since moving from Bristol City in the summer.
Boro could have made it four just before the break as Braithwaite again went clear, but his effort was skewed wide of goal as the half-time whistle blew on a delighted home crowd.
United manager Chris Wilder sent his charges out early ahead of the restart but to little avail as the Teessiders picked up from where they left off before the break.
Eventually, the Blades mustered their real chance of the game shortly before the hour mark when Leon Clarke got up well at a corner but could not guide his header on goal.
Boro stopper Darren Randolph was called into action during the latter stages of the encounter, but he successfully kept out efforts by Enda Stevens and Clarke as the hosts claimed all three points and a clean sheet.
MIDDLESBROUGH (4-3-3): Randolph; Shotton, Flint, Fry, Friend; Clayton, Howson (McNair 71'), Wing (Leadbitter 82'); Downing, Braithwaite, Assombalonga (Fletcher 78')
SHEFFIELD UNITED (5-3-2): Henderson; Baldock, Stevens, O'Connell, Basham, Egan; Lundstram (Woodburn 46'), Evans, Fleck; Clarke, McGoldrick (Duffy 69')