United central defender Chris Basham was dismissed for a second bookable offence early in the second half and former Rotherham midfield star Richie Smallwood received a straight red for a reckless challenge on Sharp before the Blades striker struck in the 73rd and 77th minutes in front of a 27,384 attendance.
The icing on the cake was provided by a third from strike partner David McGoldrick in the 82nd minute.
It was certainly a case of continuity triumphing over rotation in this feisty festive encounter.
Chris Wilder named an unchanged side for the fourth successive match and central defender Jack O'Connell made his 100th consecutive league start for the Blades.
In contrast, Rovers chief Tony Mowbray made seven changes from the side which lost in stoppage time at Leeds United on Boxing Day.
Harrison Reed, Smallwood, Joe Rothwell, Ben Brereton, who had recovered from illness, Lewis Travis, in for his first league start, Elliott Bennett, in for right-back hamstring victim Ryan Nyambe, and Kasey Palmer came into the side.
Rovers fielded a strong bench featuring Jack Rodwell, Adam Armstrong, Bradley Dack, Danny Graham and Corry Evans.
O'Connell was caught in the face early on and defensive partner Basham collected a booking for a late challenge on Reed.
Mark Duffy volleyed wide and Rovers captain Charlie Mulgrew saw his free-kick deflected for a corner in an otherwise quiet start from both sides.
Mulgrew got another chance from 24 yards and this time his free-kick struck the base of Dean Henderson's left-hand post.
The Blades were stung into life and John Fleck fed the overlapping Enda Stevens to smash a shot against the bar with 26 minutes gone.
Oliver Norwood was next into the book for a foul on Travis before the half ended goalless after a drive from Mark Duffy had been held by David Raya.
Neither side made a change for the second period.
John Egan became the third Blade in the book for a trip on Brereton but worse was to follow as Basham, standing in the defensive wall, was deemed to have handled Mulgrew's free-kick and was sent off for a second bookable offence in the 51st minute.
Wilder acted by replacing Duffy with central midfield man Paul Coutts and switching to a back four.
Referee Anthony Taylor drew ironic cheers when he booked Kasey Palmer for diving.
Henderson prevented Blackburn going ahead when he went down to his left to push a low drive from Derrick Williams around the post for a corner.
Mowbray made a double change in the 69th minute, bringing on on Armstrong and Dack for Palmer and Brereton.
Sharp received a yellow for a trip on Travis but the Blades captain was the victim of a lunging challenge from Smallwood, who received a straight red in the 71st minute.
Sharp made them pay as he latched on to David McGoldrick's header across the six-yard area to fire the Blades ahead two minutes later.
Joe Rothwell should have been booked for diving in the area but play was waved on as the Blades countered and Sharp was there waiting for the ball to drop as he fired across Raya to make it 2-0 in the 77th minute for his 16th goal in all competitions.
McGoldrick made it game over in the 82nd minute, chesting the ball in after Fleck had pinched possession in the area before whipping in a cross from the right.
McGoldrick also went in the book before being replaced by Conor Washington as Sharp gave way to Leon Clarke.