GRAHAM Dorrans' 30-yard rocket propelled Albion through the 40-points barrier - and sealed their fourth win in five home games.
The Baggies shaded this tight-but-entertaining contest - with plenty of chances at both ends - thanks to the Scotland international's second goal of the season in the 22nd minute.
The result came on the back of Albion's fourth clean sheet in five Hawthorns fixtures and sentenced relegation-threatened Rangers to a fifth successive away defeat.
Albion suffered a blow before a ball had been kicked when defensive linchpin Jonas Olsson hobbled out of the pre-match warm-up with a groin problem. Craig Dawson was elevated from the bench and James Hurst, the day's 19th man, became a sub.
The other changes from Wednesday's defeat at Manchester City saw fit-again trio Chris Brunt, Jerome Thomas and Liam Ridgewell, plus Gareth McAuley, Marc-Antoine Fortune and Peter Odemwingie, come in for Keith Andrews, Shane Long, Paul Scharner, Nicky Shorey and Simon Cox.
Mark Hughes made one change as Shaun Derry returned from suspension in place of the benched Akos Buzsaky.
The Baggies started the game in a far more comfortable position than their visitors as 13th entertained 16th, separated by eight points.
The Championship title-holders were only two points clear of the drop-zone - but it was Mark Hughes' men who created the first chance of the game.
In only the third minute, a Dawson slip let in Bobby Zamora but the ever-dependable Ben Foster was alert to the danger and blocked the ex-Fulham ace's effort at point-blank range.
Just as good a chance came Albion's way in the eighth minute when Fortune robbed Derry and threaded through Odemwingie, who fired inches past the far post from a tight angle.
Inspired by the lively Youssouf Mulumbu, the hosts got the game by the scruff of the neck and began to keep Rangers pegged back.
And after neat possession play inside the opposition half, Odemwingie found room to try his luck from 25 yards - but his effort rose into the Smethwick End.
QPR's next notable moment came on 20 when Brunt blocked Joey Barton's goalbound effort from 18 yards after Albion had only half-cleared an Adel Taarabt free-kick from the right.
Hughes' side had clearly been happy to sit back and try to hit the hosts on the counter-attack - and this outlook proved a big factor in them conceding the game's only goal on 22.
With most of the Rangers players camped on the edge of their penalty area, Dorrans had all the time in the world to control Odemwingie's lay-off and take aim from fully 30 yards. Yet the strike was still something to behold, with Paddy Kenny managing to get his finger-tips to the Scot's right-foot rocket but unable to keep it out of his top right-hand corner.
The Hoops' next effort resulted from a jinking Taarabt run, which ended with the midfielder screwing his shot well wide from 20 yards.
Albion responded with a couple of attempts of their own. Odemwingie had the Rangers rearguard reeling with a right-wing run before firing into the side-netting from an acute angle. Moments later, Mulumbu, still Albion's driving force, saw a 20-yarder take a wicked deflection and loop into Kenny's grateful arms.
On 33, it was Rangers' turn to threaten when Samba Diakite turned smartly on Jamie Mackie's lay-off inside the box and fired into the side-netting from a tight angle.
Back came Albion and Odemwingie's 15-yard curler appeared destined for the far corner - until it cannoned off Clint Hill's frame and flew wide.
QPR only half-cleared Dorrans' resulting flag-kick and Fortune tested Kenny with a 20-yard grass-cutter.
But the Hoops almost levelled on 39. Zamora got in-between Billy Jones and McAuley to meet Mackie's pinpoint centre, only to see his header arc inches wide of the far post.
Another great QPR chance came and went two minutes later. Taye Taiwo's stunning diagonal ball put Zamora in the clear but the England international's 15-yard drive was brilliantly kept out by Foster.
But Albion weathered the Rangers pressure and a great run by Odemwingie almost led to a second Albion goal, with Anton Ferdinand's vital last-ditch block preventing the Baggies' top scorer's shot from troubling Kenny.
Moments later, McAuley directed a towering header straight at Kenny from Thomas' left-wing centre.
How this game was still 1-0 was a mystery and Rangers went close again in the final minute, with Mackie cutting in from the left and shooting narrowly wide of the near post.
The second half got underway in scrappy fashion but it was Albion who threatened first, with Dorrans shooting tamely at Kenny from 20 yards.
The Baggies went much closer on 55. Brunt fed Odemwingie whose back-heel gave Jones a clear sight of goal and the right-back's low shot beat Kenny - only to strike the near post and bounce to safety.
Rangers took a while to get going after the break, but Dawson still had to risk life and limb by getting in the way of sub Shaun Wright-Phillips' 15-yard volley from Zamora's centre.
Albion suffered another injury setback on 59 when Fortune limped off and was replaced by Long. Moments later, Taarabt's corner fell nicely for Barton just inside the box, but the ex-Newcastle ace was well off target with a right-footed shot.
Rangers were now enjoying a purple patch but Barton again failed to trouble Foster's goal with a 20-yard snapshot.
At the other end, Long had livened up Albion's attack and he was unlucky to see his goalbound shot from Odemwingie's lay-off blocked by Barton in the box.
Another great chance fell to Zamora on 75 when Taarabt cut the ball back to him 12 yards out, but the former Spurs man fluffed his lines and his wayward effort struck Mackie and dribbled wide.
At the other end, Kenny was well positioned to pluck Brunt's 25-yard free-kick out of the air.
Rangers predictably threw men forward, and high balls into the box, during the closing stages, but the Baggies' rearguard defended their lines manfully.
In fact, it was Albion who went closest to scoring when, in the 92nd minute, sub Andrews slipped Long through the middle. The Republic of Ireland star advanced into the box but with Nedum Onuoha leaning into him, the off-balance striker shot wide of the target.
Referee Jonathan Moss' final whistle moments later ended any doubts about the victory, which came on the back of a thoroughly professional performance from the Baggies.
ALBION (4-4-2): Foster; Jones, McAuley, Dawson, Ridgewell; Brunt, Mulumbu, Dorrans (Andrews 70), Thomas (Scharner 81); Odemwingie, Fortune (Long 59). Subs not used: L Daniels (gk), Hurst, Shorey, Cox.
QPR (4-5-1): Kenny; Onuoha, Ferdinand, Hill, Taiwo (Traore 77); Mackie, Taarabt (Helguson 75), Derry (Wright-Phillips 57), Diakite, Barton; Zamora. Subs not used: Cerny (gk), Gabbidon, Buzsaky, Young.
GOALS: ALBION - Dorrans (22).
BOOKINGS: ALBION - Mulumbu (foul 50), Ridgewell (time-wasting 61), Dorrans (foul 70). QPR - Diakite ( foul 56).
REFEREE: J Moss (West Yorkshire)
ALBION STARMAN: Youssouf Mulumbu.