The French international set Chelsea on their way to an ultimately comfortable success with a strike in first-half stoppage time - sparking a flurry of four goals in 14 minutes.
Albion, with just one win so far this season and reeling from the loss of Gary Megson in midweek, battled gamely but finally lost their unbeaten home record.
Chelsea started sluggishly and could have fallen behind after just three minutes when Petr Cech was forced to save Robert Earnshaw's effort.
Albion enjoyed plenty of possession but their finishing let them down with Kanu failing to get his close-range shot on target in the 13th minute before Earnshaw fired wide six minutes later.
As the half wore on Chelsea began to dictate more of the play and it was no real surprise when their pressure finally told in first-half stoppage time.
Frank Lampard whipped in a right-wing free-kick for the unmarked Gallas to force the ball over the line from close range.
Having waited so long for his goal, Gallas almost added to it five minutes into the second half when his 25-yard drive was well saved by Russell Hoult.
But Chelsea only had to wait 60 seconds to increase their advantage when a cross from Damien Duff was steered home by Eidur Gudjohnsen from seven yards for his sixth goal of the season.
That looked to be the sign for Chelsea to cruise to victory. Albion were, however, determined not to go down without a fight and Zoltan Gera gave them hope after 55 minutes.
Cech was unable to hold a drive from Kanu and the rebound flew straight to Gera whose 20-yard left-footed shot whistled straight into the bottom corner of the net.
Unfortunately for Gera, he then played a part in Chelsea's decisive third goal when he slipped on the edge of the Londoners area to give away possession.
A swift counter-attack saw Lampard pick out Duff who rifled his angled left-foot drive past a stranded Hoult from the edge of the area.
Lampard then made it 4-1 with a 25-yard strike nine minutes from time after being set up by a pinpoint cross from Arjen Robben.
MAN OF THE MATCH: Frank Lampard (Chelsea) - Was rewarded for another tireless display with a late goal but his overall contribution was immense.