Hector Bellerin opened the scoring in the 37th minute with a lovely effort on his left foot, cutting in from the right to fire beyond Simon Mignolet, before Mesut Ozil struck a delightful free-kick past the Liverpool keeper's right hand three minutes later.
Alexis Sanchez then powered a sizzling effort into the roof of the net after controlling Aaron Ramsey's pass superbly before Liverpool pulled one back with just under 15 minutes left when Jordan Henderson converted from the spot after Bellerin had brought down Raheem Sterling in the area.
But the Gunners were yet done as Olivier Giroud got in on the act in injury-time with his 10th goal in his past 10 outings to make it six scoring outings on the trot after Emre Can had been sent off for a second bookable offence.
The Frenchman slotted home from close range after a defensive error from the Potters to give Chelsea all three points which looked unlikely when Charlie Adam brilliantly cancelled out Eden Hazard's 39th-minute penalty with a Goal of the Year contender from inside his own half.
However, it wasn't enough as Mark Hughes' 10th-placed side lost their third fixture in a row by a single-goal margin.
Louis van Gaal's side leapfrogged crosstown rivals City into third spot with their fifth triumph in a row.
In other matches, Everton edged Southampton 1-0 at Goodison Park, Leicester City kept their survival hopes active with a last-gasp 2-1 result over West Ham United at home while Bafetimbi Gomis scored twice to lead Swansea City to a 3-1 win over Hull City.
And in the Tyne-Wear derby, Sunderland landed a fifth-straight winning result over their arch rivals Newcastle United thanks to Jermain Defoe's world-class volley on the stroke of half-time which gave them a 1-0 win.
Monday night sees 12th-placed Palace host reigning champions City who dropped to fourth after Arsenal and United won.
2014/15 Barclays Premier League - season scores
West Bromwich Albion: 1 (Victor Anichebe 58', red card: Youssouf Mulumbu 84') QPR: 4 (Eduardo Vargas 15', Charlie Austin 37', Bobby Zamora 43', Joey Barton 90+5') The Hawthorns, West Bromwich - 25,735