Rangers have taken only two points out of a possible 21 and they were always facing an uphill task after early goals from James Morrison and Zoltan Gera. They showed signs of improvement after Adel Taarabt had reduced the arrears but Youssouf Mulumbu made it 3-1.
An injury-time effort from Esteban Granero again cut the deficit, but Albion held on for their fourth home win, their best start to a top flight season in front of their own fans since 1919, while QPR were condemned to their fifth defeat in seven games.
Albion's acting skipper Jonas Olsson received a standing ovation from the home fans before kick-off after signing a new four-year contract - and his side needed only four minutes to go ahead.
Baggies leading scorer Shane Long was too quick for Clint Hill before delivering an inviting right- wing cross. Morrison timed his run perfectly to get behind Anton Ferdinand and direct his header back across goalkeeper Julio Cesar into the corner of the net.
Albion looked sharp going forward and Long missed a golden chance to double their lead in a lightning counter-attack, firing over Morrison's cross from six yards.
It was 2-0 after 22 minutes, though. Morrison again supplied a ball into the danger area and Ferdinand's attempted clearance fell straight to Gera, who made no mistake from 10 yards.
Albion right-back Gabriel Tamas was booked for bringing down Adel Taarabt before the QPR midfielder gave his side a lifeline with a stunning finish after 35 minutes, volleying an Esteban Granero ball past Ben Foster.
The visitors showed attacking intent at the start of the second period and Foster held a low drive from the impressive Taarabt. Morrison then had a shot deflected wide before Granero had the chance to level matters - but sliced his shot wide after more good work by Taarabt.
Morrison almost capped another top performance with a second goal as his 35-yard drive flashed inches wide. With five minutes left Youssouf Mulumbu made it 3-1 after exchanging passes with Jara Reyes but QPR showed plenty of spirit and Granero reduced the gap again in injury-time with a cool finish.