Dyer struck with a left-foot shot with just seconds to go after Shane Long had put West Brom in front in a cup tie lacking in guile.
The draw keeps QPR's rejuvenation going following their midweek Barclays Premier League victory against Chelsea. QPR boss Harry Redknapp, however, also had goalkeeper Julio Cesar to thank for making a series of fine saves which included parrying a point-blank header from West Brom striker Romelu Lukaku.
Redknapp handed a debut to 30-year-old Israeli defender Tal Ben Haim, who he signed earlier in the week to try to shore up his defence.
During a first half, which for large swathes was devoid of quality, one lovely turn by Adel Taarabt to bamboozle Chris Brunt was the only real clue that this was an encounter between two Premier League sides.
In the main QPR were reduced to long-range shots, two from Taarabt which failed to test West Brom goalkeeper Boaz Myhill while Stephane Mbia sent one rasping drive skimming over the crossbar.
QPR huffed and puffed and Ji-Sung park's work ethic caught the eye in midfield but when it came to penetration it was West Brom who demonstrated why they lie seventh in the Premier League, 15 points above relegation worries while rock-bottom QPR trail the rest by five points.
In the 27th minute James Morrison shot into the arms of Cesar and the midfielder then stabbed a six-yard chance wide of the post when it looked easier to score. But it was Lukaku who gave QPR's defence the biggest headache and he was a constant threat all afternoon.
There was an extra bite and urgency to the game after the break, no doubt both managers having stressed at half-time that neither wanted a replay.
When West Brom's goal came it had a touch of fortune. QPR might have cleared the ball on a couple of occasions but it broke to Shane Long wide in the penalty area and his crisp shot took a deflection off defender Nedum Onuoha to beat Cesar. Then came Dyer's late, late strike. Perfectly executed, but in truth barely deserved.