LAST-GASP Simon Cox earned never-say-die Albion a point as the Baggies bounced back from a two-goal deficit in dramatic fashion.
A Jonas Olsson own goal and a Kaspars Gorkss header inside six early second-half minutes gave Rangers an undeserved stranglehold on the game.
Albion were in control for large chunks of the fixture and man-of-the-match Jerome Thomas pulled a goal back in the 67th minute - his sixth strike in just nine league appearances.
And top scorer Cox completed the comeback with virtually the last kick of the game when he showed ice-cool composure to steer home an awkward volley in the 94th minute - his seventh in as many games.
It was no less than Roberto Di Matteo's men deserved, with their overall display warranting a victory.
Still, the point was enough to open up a three-point gap on third -laced Cardiff, with the Baggies aboasting a superior goal difference.
Thomas, Moore and Mattock returned from injury as Di Matteo made four changes to his starting XI.
Dean Kiely was also granted his first league start of the season, with the suspended Scott Carson, Youssouf Mulumbu, Roman Bednar and Marek Cech the men to make way.
QPR also made four changes, with ex-Albion loanee Jay Simpson, Gorkss, Tom Williams and Adel Taarabt coming in for Fitz Hall, Rowan Vine, Alejandro Faurlin and Gary Borrowdale.
Second-placed Albion started the day 12 places and ten points better off than QPR who were without the services of suspended manager Jim Magilton.Youth team bosses Steve Gallen and Marc Bircham took charge.
Albion started on the front foot and Chris Brunt wasn't too far away with an ambitious third-minute volley after Moore had flicked on Olsson's lofted ball.
Two minutes later, Thomas tried his luck from distance but also was off target.
With Hoops keeper Radek Cerny putting his side under needless pressure with some dodgy kicking, the Baggies rustled the wrong side of the net on ten when Abdoulaye Meite tried to poke home Brunt's miscued corner.
Albion really should have converted their early pressure into a goal on 15 when Mattock found the unmarked Cox with a peach of a cross.
But the former Swindon striker uncharacteristically spurned the chance, heading weakly into the ground and straight at Cerny from six yards.
Rangers slowly took a foothold in the game and Kiely was the first keeper called into action in the 24th minute when he pushed away Taarabt's powerful 25-yard drive.
But Albion created another clear opening two minutes later when the ball broke neatly for Thomas after Moore had been upended by Damion Stewart.
However, the usually clinical winger never looked composed as he approached the Rangers box and shot weakly at Cerny, who clawed the ball to safety at the second attempt.
Cox was just as guilty a minute later when he failed to connect properly with a slightly more difficult opportunity after more great hold-up play by Moore.
Rangers were making life tough for the Baggies by getting virtually every man behind the ball and it took a gorgeous defence-splitting pass by Brunt to create the hosts' next opening on 32.
Unfortunately, the marauding Gianni Zuiverloon was less precise with his shot, firing a yard over from an acute angle.
QPR didn't record another shot at goal until the 36th minute when Kiely was able to watch Mikele Leigertwood's 30-yard effort sail well wide.
Back came Albion and Cerny had to show a safe pair of hands to clutch Mattock's fine 25-yard drive after the left-back had cut inside.
Albion kept prodding and probing but Thomas failed to trouble Cerny with a difficult 20-yard volley.
The Baggies had a minor scare just before half-time when lone striker Patrick Agyemang got the wrong side of Meite to control Williams' hopeful punt forward.
But after turning back from the byline, the former Preston striker could only fire tamely into the side-netting from an acute angle.
Thomas still looked the man most likely to unlock the Hoops defence and after leaving Peter Ramage on his back-side, his low cross just evaded the outstretched boot of Moore in the six-yard box.
Albion made a rip-roaring start to the second half and, after only 45 secs, Gorkss had to come to Cerny's rescue by clearing before Moore and Cox could pounce after the Hoops keeper had spilled Brunt's ferocious 20-yard drive.
But completely against the run of play, it was the West Londoners who took a somewhat fortuitous lead.
Ben Watson swung in a 56th-minute corner and the off-balance Olsson, who appeared to be pushed by Gorkss, saw the ball loop off the back of his head, soar over Graham Dorrans at the far post and into the net.
Incredibly, Rangers almost made it 2-0 60 seconds later when Kiely brilliantly pushed Taarabt's stunning 20-yard effort onto his bar and the ball bounced to safety.
But QPR did double their lead in the 62nd minute - and again there was a huge slice of luck involved.
Kiely pushed away Watson's dangerous free-kick, only to see the ball rebound off Mattock and fly straight to Gorkss who had the simple task of heading into an empty net.
This had by no means been a perfect Baggies display, but finding themselves 2-0 down smacked of injustice.
The hosts regrouped and Cox wasn't too far away with a spectacular 25-yard shot which swerved just wide.
But Thomas did give Di Matteo's men a lifeline by pulling a goal back on 67.
Brunt managed to head Dorrans' deep centre back into the mixer and after sub Chris Wood and Cox challenged, the ball broke to Thomas who swept home under Cerny to score for the third successive match.
The game had well and truly burst into life and it took another stunning one-handed save from Kiely, this time to divert wide Wayne Routledge's 18-yard effort, to prevent Rangers regaining their two-goal cushion.
Thomas continued to prove a thorn in Rangers' side and a terrific left-wing run resulted in him dragging a 20-yard shot wide of the near post.
Albion went even closer in the 79th minute when Wood flicked on Dorrans' ball into the box and Zuiverloon saw his header loop past Cerny, only to hit the foot of the post and bounce out of play.
The agony continued two minutes later when Cerny pulled off a stunning one-handed save to push over Cox's sweet turn and volley.
But Albion kept going right to the death and got their just desserts in the 94th minute.
Sub Bednar pumped a high ball forward and Wood used all of his brute strength to hold off four defenders and volley goalwards form 18 yards.
Cerny did well to parry the ball but it flew straight to Cox who showed great composure to steer it into an empty net.
ALBION (4-4-2): Kiely; Zuiverloon (Bednar 85), Meite, Olsson, Mattock; Brunt, Dorrans, Jara, Thomas; Moore (Wood 65), Cox. Subs not used: Allsop (gk), Martis, Teixeira, Cech, Mulumbu.
QPR (4-4-1-1): Cerny; Ramage, Gorkss, Stewart, Williams; Routledge, Leigertwood, Watson, Simpson (Hall 90+2); Taarabt (Faurlin 82); Agyemang (Pellicori 84). Subs not used: Taylor (gk), Vine, Alberti, Parker.
GOALS: ALBION - Thomas (67), Cox (90+4). QPR - Olsson (own goal, 56), Gorkss (62).
BOOKINGS: ALBION - Brunt (dissent 84).
REFEREE: A Taylor (Cheshire).
ALBION STARMAN: Jerome Thomas.
PIC: LATE LATE SHOW...Cox steers home his last-gasp equaliser