Had every managerial change at Loftus Road had this effect, Rangers would have had the title sewn up long ago.
As it is Warnock, the club's fifth new boss this season, will be happy the west Londoners now have a little more breathing space above the relegation zone.
Chris Brunt pulled one back for Albion but they fell to a costly defeat which leaves them nine points behind Newcastle at the top of the Championship.
Warnock's teams have rarely been known for their flair but his first selection decision was to recall the hugely skilful, yet too often frustrating, Tottenham loanee Adel Taarabt.
The Moroccan midfielder began in his usual blur of stepovers on Saturday and created the first goal for Simpson after 13 minutes.
He bamboozled Ben Watson down the right before swinging a low cross into the six-yard box which Albion keeper Scott Carson spilled at the feet of Hogan Ephraim.
Carson blocked Ephraim's stab at goal but the ball fell to Simpson, once of Albion, and he took a touch before firing his 13th of the season past the stranded keeper.
Five minutes later the vibrant hosts doubled their lead, Alejandro Faurlin's clever crossfield pass finding right-back Connolly in acres of space to slot the ball through Carson's legs.
Shell-shocked Albion took half an hour to muster up their first attack when Watson, who played for Warnock at Palace and had a loan spell at Rangers earlier this season, hit a volley from the edge of the area which was superbly clawed away by Carl Ikeme.
But the team with the best away record in the division were always going to be dangerous against a team who had not kept a clean sheet in 23 games.
And so it proved in the 35th minute when Jerome Thomas crossed from the left and Brunt looped a header back over Ikeme and into the net.
In the second half Simon Cox felt he should have had a penalty when he tumbled under Kaspars Gorkss' challenge, but young referee Stuart Atwell saved himself from an earful from Warnock by waving away the claims.
And Warnock was able to relax on the touchline when substitute Buzsaky put the hosts clear in the 67th minute with a curling free-kick, which was meant to be a cross but fooled Carson and flew in off the far post.
The Baggies' afternoon got worse in stoppage time when Cox had to be stretchered off.