After a quiet opening Hogan Ephraim set up Angelo Balanta to fire Rangers ahead from the edge of the six-yard box.
Lee Camp produced a fine save to deny James Beattie's volley and Ephraim shot wide but chances were at a premium.
Balanta's shot was saved by Paddy Kenny after the break before Morgan fired home in what was the last clear-cut opportunity as both defences held firm.
Sheff Utd boss Kevin Blackwell:
"I thought we thoroughly deserved the equaliser and we should have gone on to win. "QPR knew how to play the pitch and the windy conditions and, once we worked it out in the second half, we improved a lot.
"We definitely had more chances after the break and I brought two strikers and a wide-man on to try to win the game - we have to go for it like that if we are to have any chance of making the play-offs."
QPR: Camp, Mancienne, Connolly (Stewart 73), Hall, Delaney, Ephraim, Rowlands, Leigertwood, Balanta (Blackstock 73), Vine, Agyemang.
Subs Not Used: Pickens, Lee, Rehman.
Goals: Balanta 19.
Sheff Utd: Kenny, Geary, Morgan, Kilgallon, Naysmith, Stead (Shelton 77), Tonge, Armstrong, Quinn, Sharp (Cotterill 70), Beattie (Hulse 77).
Subs Not Used: Gillespie, Lucketti.
Booked: Morgan, Geary.
Goals: Morgan 78.
Att: 15,383
Ref: Steve Bennett (Kent).
E-mail this to a friend 
Printable version 
Bookmark with:
What are these?