Eduardo Vargas and Charlie Austin were on target before Bobby Zamora scored the pick of the bunch to put the visitors 3-0 up at the break.
Victor Anichebe reduced the deficit at The Hawthorns, but Youssuf Mulumbu's red card dashed home hopes of a comeback and Joey Barton added the fourth to give Ramsey only his second win at the helm, with QPR now just one point from safety.
"We've been close to that – performance-wise – for a while, we just haven't taken the chances in the same way," head coach Ramsey said.
"We scored some really good goals today, but we've missed easier chances than that in the last few games as well.
"We were disappointed letting a goal in because we wanted to keep a clean sheet – we need to focus on keeping the edge in front of goal, but also avoiding silly mistakes at the back – we do that and we're well in contention to stay up."
Rangers now face a huge match at Aston Villa on Tuesday, with Tim Sherwood's side - 3-1 losers at Manchester United - only three points above them.
