QPR skipper Kevin Gallen scored with a smart finish to give the visitors the lead, though soon after Adam Hinshelwood slammed home an equaliser.
Darren Currie gave Brighton the lead with a well-executed free-kick, just after he had rattled the crossbar with an identical effort 20 yards from goal.
A tap in from Paul Furlong - who also hit the woodwork with a header - made it 2-2, before Rose snatched the win.
Brighton manager Mark McGhee:
"The most important thing to me is my performance and I had a bad game today because I couldn't see how to change it when things were going wrong.
"At half-time we looked really comfortable and I couldn't see us being in much trouble. But we were then poor and I had a stinker.
"At 2-1 down we couldn't see what to do. We had four people on the bench who could have stemmed the tide and I took too long to react - I got it wrong."
QPR manager Ian Holloway:
"We knew it would be tough against Brighton because they have spirit and desire but I'm also seeing those qualities from my players at the moment."
"Confidence and belief is coming through for us. We had terrible injury problems at the start of the season, but we know where we are going.
"And Paul Furlong has been absolutely determined to be even better every day. His attitude is magnificent on and off the pitch."
Brighton: Kuipers, El-Abd (Jarrett 82), Mayo, Cullip, Harding,
Currie, Nicolas (Knight 87), Hinshelwood,
Hammond (Carpenter 86), Virgo, McPhee.
Subs Not Used: Oatway, May.
Goals: Hinshelwood 23, Currie 44.
QPR: Day, Bignot, Rose, Santos, Padula (Edghill 71), Cureton,
Rowlands (McLeod 71), Bircham, Cook (Shittu 78), Gallen,
Subs Not Used: Johnson, Cole.
Goals: Gallen 16, Furlong 74, Rose 90.
Ref: B Curson (Leicestershire).