Luke Freeman's 60th-minute strike meant Town's 1,746 travelling fans in a 14,044 crowd had to endure a tense finale, and their celebrations after seven minutes of time added on reflected the importance of this latest success.
QPR worked hard to get the ball up towards big Matt Smith, their recent signing from Fulham, but were undone by clinical strikes by Brown and Wells.
It was Wells who crossed for on-loan Chelsea forward Brown to claim his fourth Town goal in the 26th minute.
Home boss Ian Holloway made a double change on 53 minutes, and one of his new faces Freeman struck with a powerful shot on the hour to get his side back into the game.
Danny Ward made a great save to thwart Smith on 70 minutes then used his feet block from Yeni Ngbakoto in stoppage time.
1min: Izzy Brown's shot is saved by former Town keeper Alex Smithies.
5mins: Jake Bidwell fires over for QPR after a corner is cleared.
8mins: Danny Ward pushes Conor Washington's shot against his right-hand post and out for a corner, from which Matt Smith's header is held by the Town stopper.
13mins: Smithies smothers the ball as Nahki Wells lurks.
14mins: QPR striker Smith volleys over.
24mins: Ryan Manning's shot for the hosts is too high.
26mins: Brown shoots Town ahead from a Wells cross. 0-1.
37mins: Wells puts Town two to the good with a precision strike after Elias Kachunga touches on a Martin Cranie cross. 0-2.
42mins: Chris Lowe's free-kick is headed clear by QPR.
54mins: Washington goes down under Kachunga's challenge, but no penalty for the hosts.
57mins: A Washington cross just evades Smith.
60mins: Luke Freeman drills in a shot from inside the area for QPR. 1-2.
65mins: Town's Rajiv van La Parra shoots wide from distance, then Wells is only just off target from closer in.
70mins: Ward makes a great save to deny Smith a leveller.
72mins: Successive free-kicks are drilled into the Town wall by Manning and Kazenga LuaLua.
78mins: Manning's cross is cleared by Town.
90+5mins: Ward blocks a Yeni Ngbakoto shot with his feet.
QPR: Smithies, Bidwell (Freeman, 53), Hall, Perch, Onuoha, Luongo, Wszolek (Ngbakoto, 78), Manning, Washington, Smith, Mackie (LuaLua, 53).
Subs not used : Goss, Furlong, Sylla, Ingram.
Town: Ward, Cranie (Smith, 78), Hefele, Schindler, Lowe, Hogg (Billing, 20), Mooy, Kachunga, Brown, Van La Parra (Lolley, 78), Wells.
Subs not used: Payne, Quaner, Stankovic, Coleman.
Referee: Peter Bankes (Merseyside).