Keith Andrews scored his first goal for 10-man Blackburn Rovers to salvage a point against Tony Mowbray's side at The Hawthorns.
Andrews, signed from MK Dons in August for £1.3m, drilled a low 20-yard cross-shot past Baggies goalkeeper Scott Carson.
Striker Benni McCarthy put Blackburn ahead from the penalty spot before being sent off for two bookable offences.
Goals from Roman Bednar and Ishmael Miller looked to have sealed victory for Albion before Andrews' late strike.
McCarthy had given Rovers a first-half lead from the penalty spot but was then dismissed by referee Mike Jones for two bookable offences before half-time.
Albion dominated the second period and Bednar brought them level before Miller struck for the second time in five days for Mowbray's side.
It looked as if the Baggies were going to gain a precious win after a run of three successive defeats had sent them veering towards the Barclays Premier League relegation zone - but Andrews clean hit spoilt their day.
finished article
Miller justified Mowbray's decision to promote him to the starting line-up after breaking his duck for the campaign against Newcastle United in midweek.
And the quality of his goal against Rovers suggests there is a talent waiting to be unleashed once he fully adjusts to the demands of the top flight, although he still has much to learn before being the finished article.
After 11 minutes Paul Ince's side went ahead after Ryan Donk needlessly conceded a penalty.
There appeared to be little danger but Donk, who had also given away a penalty at Newcastle, tugged at the shirt of former Albion striker Jason Roberts.
Up stepped McCarthy and the power of his shot ensured it nestled in the corner of the net even though Carson dived the right way.
Rovers 'keeper Paul Robinson beat out a fierce volley from James Morrison, then Borja Valero chipped over the bar, before McCarthy picked up the first of his yellow cards after 19 minutes for bringing down Greening.
Robert Koren was also off target, before McCarthy handled a 36th-minute clearance from Olsson near the halfway line and was sent off.
Donk was then booked for returning to the action without permission after receiving treatment on the touchline.
swerving attempt
Carson had to be alert to turn aside a swerving attempt from Emerton in first half injury-time while Robinson went down to his left to cling on to a drive from Miller in the final seconds of the half.
Blackburn had a remarkable let-off when Miller hit the post with a left foot shot, then Rovers defender Ryan Nelsen inadvertently deflected the ball against the bar and the upright before the danger was cleared.
Robinson did well to beat out a 25-yard Koren piledriver but Rovers were under the cosh and after 55 minutes Bednar brought the hosts level.
Valero and Miller were involved in the build-up before releasing Bednar, who poked the ball past Robinson for his fourth goal of the campaign.
Blackburn seemed powerless to stop the tide of attacks towards their goal and after 62 minutes a superb strike by Miller put the Baggies in front.
Valero played the ball into the feet of Miller and in an instant he spun on the edge of the box and crashed a fierce low shot past the dive of Robinson into the corner of the net.
Albion looked as if they were going to take full honours - but with seconds remaining they were denied when Andrews' angled drive sped past Carson.