Prior to Saturday's meeting at The Hawthorns, QPR had lost 13 of their 14 away league games this season, but they showed a clinical edge in the opening period as Eduardo Vargas, Charlie Austin and Bobby Zamora all found the net.
Vargas, rewarded with a starting spot after coming off the bench to score in the 2-1 defeat to Everton last time out, repaid the faith shown in him by Ramsey with a swerving long-range effort to break the deadlock.
Austin, who netted a hat-trick in QPR's 3-2 win at Loftus Road in the reverse fixture back in December, then headed in from a corner before Zamora's stunning chip capped an impressive first 45 minutes from the visitors.
West Brom had kept clean sheets in six of their seven previous home games across all competitions since Tony Pulis took over in January, and their performance was met by a chorus of boos at the interval.
Pulis reacted by introducing Victor Anichebe for Stephane Sessegnon at the break and the striker's header just before the hour mark gave West Brom brief hope, but that disappeared when substitute Youssouf Mulumbu was sent off six minutes from the end and then Joey Barton added a fourth for QPR in injury time.
West Brom had Brown Ideye back in the side after a knee problem and he sent a free header off target before Vargas put the visitors ahead in the 15th minute.
The Chilean picked up the ball from Austin and, as the West Brom defence backed off, he unleashed a 25-yard shot that flew into the bottom-left corner.
Ideye almost scored an equaliser four minutes later, although he knew little about it as Chris Baird's whipped cross struck his leg and flew wide of the right-hand upright.
QPR suffered a blow on the half-hour mark when Vargas twisted his knee and had to be replaced by Niko Kranjcar, who soon had a telling impact in flicking on Matt Phillips' right-wing corner for Austin to nod home unmarked at the far post.
West Brom were stunned, and two minutes before the break they fell further behind. Zamora ran onto Phillips' ball down the right channel and, from the corner of the box, lofted a superb finish with the outside of his left foot over Boaz Myhill and in off the crossbar.
The home faithful vented their frustration at half-time, but their mood was improved 13 minutes into the second period when Anichebe rose to head in Saido Berahino's cross from the left.
Anichebe was causing problems for the visiting defence, and his knockdown fell to Ideye whose strong drive was parried by Rob Green.
QPR felt they should have had a penalty when Zamora's cross struck James Morrison's arm, before Ideye brought another save out of Green with a fierce volley from 20 yards.
Berahino ought to have further reduced the deficit 10 minutes from time, but his free header from six yards was weak and comfortable for Green, before Ideye flicked Chris Brunt's cross narrowly over.
Mulumbu, on as a 72nd-minute substitute for Craig Gardner, was dismissed six minutes from time after leading with his arm in an aerial challenge with Barton, catching the QPR man in the face.
In the final minute of stoppage time, Barton completed the scoring with a left-footed drive following a scramble in the box as QPR ended a run of five consecutive defeats to move above Burnley into 18th in the table.
