Miller ran from deep before slotting a low shot past goalkeeper Steve Mildenhall to give the hosts a fourth-minute lead at Bramall Lane on Boxing Day.
Scunthorpe went close to equalising before the break when Damien Mozika's header came back off the crossbar and George Long saved Andy Barcham's follow up.
Long also kept out a Tom Newey free-kick towards the end of the first half while, at the other end, Miller had a shot deflected wide.
Kitson extended the Blades' lead after 56 minutes, meeting Tony McMahon's free-kick with a firm header.
After Newey was adjudged to have fouled Ryan Flynn in the area, Blackman rounded off the scoring from the penalty spot with six minutes remaining.