The Hungary international was not in the visitors' matchday 18 due to injury, but temporary managers Steve Gallen and Marc Bircham looked to have enjoyed a debut to remember.
For all Albion's dominance, they failed to punish the visitors and a Jonas Olsson own goal was quickly followed up on the hour mark by Kaspars Gorkss' header.
But West Brom never gave up and Jerome Thomas reduced the deficit before Cox's late, late leveller.
The result leaves Rangers without a win in eight games while second-placed Albion have stretched their advantage over the chasing pack to four points.
QPR keeper Radek Cerny endured a nightmare start as he made a complete hash of three attempted clearances. But he was not alone in looking unsettled as the majority of his team-mates looked at sixes and sevens during the opening stages.
The first chance of the encounter fell to Cox after 15 minutes but he could only head Joe Mattock's left-wing cross straight at Cerny from close range when he really should have done better.
Impressive on-loan midfielder Adel Taarabt forced a solid parry from Dean Kiely at the other end, who was taking his place between the sticks due to Scott Carson's suspension.
Despite his nervy start, Cerny proved his worth for the visitors after 26 minutes when he got half a hand on Thomas's shot after he found himself one on one.
And then with the ball trickling to the line, the Rangers stopper recovered to his feet to push it to safety.
Gianni Zuiverloon fired well over when played into a great position by some neat approach play and an incisive throughball from Chris Brunt - summing up the first half in a single move.
The visitors barely managed to get out of their own half in the early stages of the second half but, in similar fashion to the opening 45 minutes, some stout defending and a lack of quality in the final third ensured it remained goalless.
And the Baggies were made to pay for their wastefulness in front of goal in the 56th minute.
Ben Watson whipped in a corner and Olsson, under pressure from Gorkss, diverted an unfortunate header over Graham Dorrans on the line and into the top corner.
Tottenham man Taarabt almost made it 2-0 just minutes later as Kiely produced a superb fingertip save to divert his 25-yard strike on to the angle of bar and post.
But the visitors did double their advantage just after the hour mark.
Watson floated a free-kick goalwards from a central position which evaded everyone.
Yet Kiely could only palm the ball into the onrushing Mattock and it subsequently fell for Gorkss to head into an empty net.
Out of nowhere the game had exploded to life and West Brom reduced the arrears just five minutes later when the Rangers defence failed to clear Brunt's knock down and Thomas pounced to smash home his sixth league goal of the season.
Albion applied a host of pressure in the closing 15 minutes with Zuiverloon's header clipping the outside of a post and Cox forcing a great stop from Cerny.
And it was the latter who rescued a dramatic point for West Brom when he pounced from close range deep into injury time.