Hulse, who had been suffering from a virus this week, found space at the far post to tap home Gary Kelly's free-kick from the left after 40 minutes.
Leeds went down to 10 men when striker David Healy was given a straight red card midway through the second half for kicking out at Marc Bircham.
But QPR failed to capitalise as Georges Santos and Paul Furlong missed chances.
Leeds boss Kevin Blackwell:
"Getting this club back to the Premiership will be a big test - and I am still finding out whether some of them are capable of passing it.
"I learned a lot about them today. They responded brilliantly to the defeat by Sheffield Wednesday.
"The 18 players we brought today were the only ones available."
QPR: Royce, Bignot, Santos, Shittu, Milanese (Evatt 29), Ainsworth (Rowlands 59), Bircham, Lomas, Cook, Sturridge (Moore 59), Furlong.
Subs Not Used: Nygaard, Langley.
Booked: Cook, Bircham.
Leeds: Sullivan, Kelly, Butler, Gregan, Crainey, Douglas, Einarsson, Derry, Lewis, Healy, Hulse (Cresswell 71).
Subs Not Used: Bennett, Pugh, Moore, Kilgallon.
Sent Off: Healy (65).
Booked: Gregan, Einarsson, Kelly, Derry.
Goals: Hulse 41.
Ref: P Walton (Northamptonshire).