The 35-year-old striker put the Blades in front after 17 minutes with a simple close-range header, while John Egan scored twice after the restart to seal a routine away victory.
Sharp's day, however, was rather soured late in the first half when his spot-kick was well saved by Matt Ingram.
That miss was not damaging, though, as Egan put clear water between the two sides with a 50th-minute header from Conor Hourihane's inswinging corner.
Hourihane and Egan repeated the dose in similar circumstances after 61 minutes when the Republic of Ireland international glanced home from the right corner of the six-yard box.
Keane Lewis-Potter made it 3-1 – Hull's first goal since the opening day of the season – after 74 minutes, but there was no way back for the Tigers.
After having made a bad start following their relegation from the Premier League, Slavisa Jokanovic's men are now unbeaten in five Sky Bet Championship games.
The hosts, by contrast, look a shadow of the all-action team that finished top of League One last season.
Their increasingly anxious supporters would at least have been satisfied by Hull's early vigour, but it did not take long before Sheffield United found a controlled rhythm.
That subtle shift in momentum helped the visitors score with their first meaningful attack.
Gibbs-White sent over a deft cross towards the edge of the six-yard box, from where Sharp could not miss.
Hull rallied, yet Gibbs-White nearly made it 2-0 when his low drive from a tight angle was well parried by goalkeeper Matt Ingram.
The Impressive Gibbs-White then played a significant role in the awarding of United's penalty.
His threaded ball found Sharp through the middle, with Jacob Greaves adjudged to have fouled the Blades forward inside the box.
Greaves appeared to take the legs of Sharp before getting a foot on the ball, but the resulting penalty, which Sharp sent low to the left, was saved.
It proved inconsequential in the context of the game as Egan made it 2-0 when he was far too strong for Hull's frail backline.
Grant McCann's men lost their discipline during a spell of Sheffield United dominance and were punished by the concession of another poor goal.
Home fans at least enjoyed seeing their team score for the first time in seven league games when Lewis-Potter bundled in Tyler Smith's low cross from the right.
The points, however, had long since been sewn up.