Loan striker Adam Armstrong's second Baggies goal, a penalty late on in the first half, proved the difference but Tony Mowbray's men were made to work hard for it in a backs-to-the-wall display as Darnell Furlong was sent off in first-half stoppage time.
Full-back Furlong was judged to have swung an elbow to QPR winger Koki Saito and referee Adam Herczeg, who has done most of his work in the lower leagues this term, gave red.
The second half was not much of a spectacle in the visitors' half, but the hosts were gritty and defensively resilience to limit the Hoops, who still had half-a-hope on a late play-off surge, to very little.
On a weekend that saw four direct rivals below Albion, Bristol City, Blackburn, Middlesbrough and Norwich, all drop points Albion crucially held on and showed they have the spirit and stomach to win a play-off race featuring at least half-a-dozen competitors.
A noticeable five point gap between the Baggies and ninth-placed Boro has been created ahead of Tuesday's difficult trip to Burnley before a home clash with Hull to sign off for the international break.
Albion started well buoyed by a good noise around The Hawthorns and the first 10 minutes showed a Hoops team struggling to find their feet.
Marti Cifuentes' men settled well, though. Evergreen skipper Steve Cook was allowed a free header from an Ilias Chair corner, which the hosts blocked well.
The Baggies' first sighter came as the wingers combined. Fellows darted away from two markers on halfway and drove through the centre of the pitch. He picked a smart pass for Mikey Johnston but the Republic of Ireland international could only curl off target while trying to pick out the top right corner.
QPR settled and by the half hour mark looked comfortable. Tricky customer Yang min-Hyeok, on loan from Tottenham, caused Callum Styles problems and creativity lacked in the middle and final third.
Mowbray's men were fortunate defender Jimmy Dunne could only turn into the side netting after the Baggies failed to clear a corner.
The first period was meandering nowhere fast as referee Herczeg pointed to the penalty spot seven minutes before the interval. The official judged Jack Colback had tripped Jayson Molumby from Tom Fellows' low cross after the winger had flown past Kenneth Paal. Furlong started the move with a neat ball down the flank.
Armstrong made no mistake from the spot as he found the left corner despite keeper Paul Nardi's fingertips.
The Hoops were rocked by the opener and Albion looked good for their half-time lead - until some stoppage-time drama.
Winger Koki Saito, who became the lively panto villain, hit the deck from a nothing long free-kick from deep in QPR territory.
Visiting black shirts quickly appealed a stray elbow to the officials and after some deliberation referee Herczeg, with apparent help from fourth official Dean Whitestone, issued a red card.
Replays were inconclusive with no angle to show the alleged incident. Some spectators close to the coming together suggested Furlong gave the referee a decision to make.
Mowbray responded at the break with defender Mason Holgate introduced for Fellows, who had been bright. QPR made a double change.
Albion struggled to get out of the traps after the interval and much of the half came about Mowbray's men digging in within a disciplined shape and defending their box well with regular deliveries from Saito and Yang.
Saito flung himself in the six-yard box to steer a diving header wide of the left post after the assistant had let go what appeared an offside.
But after that opening the hosts settled into their new shape. Holgate and Kyle Bartley picked up bookings but were disciplined thereafter. Isaac Price found himself in the Fellows-shaped right midfield hole and did a tireless job.
Chances for the Hoops dried up with Albion rigid. Tension and needle remained throughout the contest with the Baggies deep and struggling to cross the halfway line with little outball. Karlan Grant and Daryl Dike both came on to add physicality.
Albion's second half was typified by Molumby's charge from his own half to the edge of the visiting penalty area to win a free-kick.
Price was given a standing ovation early into eight minutes of stoppages for his brilliant work. For all of QPR's second-half possession Joe Wildsmith was only really stretched by a late Saito effort, which the keeper held on to well to see Albion home.
**Albion (4-2-3-1):** Wildsmith; Furlong, Bartley, Heggem, Styles; Mowatt, Molumby; Fellows (Holgate, 45), Price (Diakite, 90+4), Johnston (Grant, 62); Armstrong (Dike, 78).
**Subs not used:** Griffiths, Swift, Diangana, Bany, Lankshear.
**QPR (4-2-3-1):** Nardi; Dunne, Cook (c) (Morris, 45), Edwards, Paal (Andersen, 89); Morgan (Dembele, 69), Colback; Yang (Ashby, 89), Chair, Saito; Smyth (Lloyd, 45).
**Subs not used:** Walsh, Fox, Madsen, Bennie.
**Referee:** Adam Herczeg