Chelsea marked manager Jose Mourinho's 100th match in charge with a win to further cement their Premiership lead.
Drogba looked in impressive form for Chelsea
Having been virtually anonymous as an attacking force in the first-half, Chelsea took the lead on 50 minutes through Didier Drogba's low shot.
Chelsea were reduced to 10 men when Arjen Robben was sent off for a wild two-footed lunge on Jonathan Greening.
Joe Cole made it 2-0 from close-range, before Kanu led a late Baggies rally and slipped the ball past Petr Cech.
Chelsea's win contained all the ingredients that have characterised Mourinho's reign, lethal finishing allied to superb defensive play, sprinkled with a huge dose of controversy.
Mourinho's managerial counterpart Bryan Robson was left fuming at Chelsea's late return to the pitch at the start of the second half as the interval stretched to 18 minutes.
Robben's dismisssal for a dangerous tackle after he had lost the ball was fully deserved, while Robson and Mourinho had another bad tempered exchange just before Cole's goal.
If Chelsea were at their efficient best in the second half, Mourinho's side were altogether more sloppy in the opening 45 minutes.
After Eidur Gudjohnsen badly scuffed a shot wide in the game's first chance, Chelsea found it difficult to get out of first gear.
Chelsea's sluggish start allowed West Brom to come into the game and Kevin Campbell drew a fine save from Cech following Diomansy Kamara's free-kick.
Cech was then unable to get sufficient distance on his punch from a Greening cross and Jan Kozak went close with a lob that landed on the roof of the net.
Just before the half-hour Chelsea managed to finally test Tomasz Kuszczak, who moved swiftly to collect Damien Duff's shot.
Five minutes before the interval Kamara slalomed down the wing before cutting inside and shooting into the side-netting.
If Chelsea were sloppy in that opening half, West Brom picked up the habit after the interval with fatal consequences.
Junichi Inamoto's casual pass richocheted to Drogba and as succession of West Brom defenders stood off, the Ivory Coast striker found the corner with a low shot.
Drogba then almost grabbed a second, running on to Robert Huth's diagonal pass, before striking a half-volley that Kuszczak was unable to hold.
Having finally established some semblance control of the match, Chelsea found themselves playing the last half-hour at a numerical disadvantage after Robben was red-carded for his reckless tackle on Greening.
But West Brom shot themselves in the foot for a second time as substitute Cole was on hand to fire the ball into the net after the home side failed to clear the ball after a Drogba shot.
With two minutes to go Kanu was on hand at the near post to force the ball past Cech, but Chelsea held on to pick up another three points.
West Brom boss Bryan Robson:
"I have invited him (Mourinho) and his staff in after the game for a glass of wine. I have no qualms about it.
"That's it as far as I'm concerned.
"He is a very good coach and is doing a fantastic job at Chelsea. They grind out results. He hasn't wound me up, my team wound me up."
Chelsea captain John Terry:
"The referee was saying Arjen Robben's was a two-footed tackle but he didn't touch the man at all.
"We had a long team talk. We got a bit of a telling-off at half-time, it was what we needed.
"Our fans were fantastic, singing Peter Osgood's name, and we'd like to dedicate that win to him. He was a great man."
West Brom: Kuszczak, Albrechtsen (Watson 82), Curtis Davies, Clement, Robinson, Greening, Wallwork, Kozak, Inamoto (Ellington 71), Kamara, Campbell (Kanu 71).
Subs Not Used: Kirkland, Carter.
Goals: Kanu 88.
Chelsea: Cech, Paulo Ferreira, Terry, Huth, Gallas, Essien, Makelele, Gudjohnsen (Geremi 73), Robben, Drogba (Wright-Phillips 85), Duff (Joe Cole 63).
Subs Not Used: Cudicini, Maniche.
Sent Off: Robben (62).
Goals: Drogba 51, Joe Cole 74.
Ref: M Halsey (Lancashire).