The win leaves Neil Warnock's side just two wins away from securing a return to the top flight after a 12-year exile.
United, who had recovered from a disastrous run of one win in eight games, had squandered a two-goal lead as rejuvenated Hull hit back before 33-year-old Unsworth scored deep in injury time.
Hull, unbeaten in their last four including a victory over Leeds last week, almost found a way through in the seventh minute when midfielder Michael Tonge blundered and Keith Andrews pounced to drill a right-foot strike from 25 yards which flashed a fraction wide of the target
Danny Webber fired over before United went ahead in the 36th minute. Tonge shook off his marker and swept over a low cross which Neil Shipperley steamed in to sweep over the line from close range for his 11th of the season.
Webber almost snatched a second three minutes before the interval with a stinging drive that was pushed over the top by Boaz Myhill.
Paul Ifill grabbed the second after 53 minute as he stretched to reach a Webber cross from the left flank and finished with a textbook header from eight yards.
Stuart Elliott pulled one back in the 64th minute as he beat Paddy Kenny with a right-foot shot from six yards after United failed to cut out Alton Thelwell's deep cross.
Darryl Duffy grabbed the equaliser in the 70th minute as he bundled Stuart Green's low cross over the line.
But the Blades bounced back and Unsworth hit the winner three minutes into injury time after substitute Steven Kabba's shot had been blocked.