Half-time substitute Henri Camara immediately got United back into the game with his first touch but Kevin Blackwell's side could not find an equaliser despite making it an uncomfortable second half for the Foxes.
The result ended the Blades' seven-game unbeaten league run and left the south Yorkshire club without a league win on Boxing Day since 2004.
Former Fox Jordan Stewart had a good early chance after getting the better of Jack Hobbs but he shot straight at Chris Weale.
At the other end, Mark Bunn was called into action by his own player after Nick Montgomery inadvertently sliced a clearance goalwards.
Lloyd Dyer threatened on a couple of occasions and Bunn had to tip an ambitious long-range effort from Morrison over the crossbar.
From Matt Oakley's resulting corner, Morrison arrived unmarked inside the six-yard box to head Leicester in front after 26 minutes.
Nine minutes later Montgomery tripped Fryatt inside the area and City's leading scorer picked himself up to net his 12th goal of the season from the penalty spot.
Nigel Pearson's side would have been out of sight had Richie Wellens' shot from the edge of the box been a couple of inches lower instead of striking the crossbar in first-half injury time.
Blackwell brought on Camara for Andy Taylor at the break and it proved an inspired move as the Senegal striker scored less than two minutes after his introduction.
Stephen Quinn's ball into the box from the left was pounced on by Camara, who beat Weale from close range.
Dyer and Steve Howard forced Bunn into parries before the hour mark and Howard should have worked Bunn again soon afterwards but headed wide.
Weale then had to tip an 18-yard shot from Jamie Ward over the crossbar after 65 minutes.
Chances continued to come at both ends. United captain Chris Morgan went close with a header and Camara flashed a shot just wide either side of the midway point of the second half.
Fryatt narrowly missed the bottom corner with a curling effort from the edge of the box.
United had one last opportunity to salvage a draw but substitute Ched Evans was thwarted by Weale.