Goals from Jay Simpson and Matt Connolly put Rangers in the driving seat and after Chris Brunt netted for Albion, substitute Akos Buzsaky's fortuitous goal sealed a deserved victory for the Londoners.
Warnock had to wait only 13 minutes for Rangers' first goal of his reign.
Adel Taarabt sent in a low cross from the right and after goalkeeper Scott Carson fumbled while under pressure from Hogan Ephraim, Simpson pounced on the loose ball to score from close range.
Connolly then finished off a fine Rangers move to double their lead just five minutes later.
After neat play involving Ephraim and Taarabt, Connolly galloped forward from the right-back position to collect Alejandro Faurlin's lovely pass and fire through Carson's legs.
Albion's first sight of goal came when Brunt dispossessed Mikele Leigertwood and threaded the ball through for Simon Cox but keeper Carl Ikeme reacted quickly and gathered the ball at the striker's feet.
Ikeme also did well to push away a Ben Watson volley, but was unable to stop Albion reducing the deficit on 35 minutes.
Jerome Thomas crossed from the left, and Brunt's looping header at the far post beat Ikeme and dropped into the bottom corner.
The goal galvanised the visitors, who made a determined start to the second half.
Cox blazed wide from Brunt's cross and, as Albion continued to press, Cox appealed in vain for a penalty after going down under Kaspars Gorkss' challenge.
Warnock brought on Buzsaky to try and regain the initiative, and it was the Hungarian who restored Rangers' lead - albeit with a slice of luck.
Buzsaky 35-yard free-kick from the left was meant for the head of Gorkss but evaded everyone - including Carson - and struck the inside of the far post before trickling over the line.
Simpson had a chance to make it four, but miscued after being put through by Rowan Vine.