The Blues remain unbeaten after 12 games this season, winning ten and drawing two after this weekend's win, leaving them top of the table with 32 points.
Here are some of the images that tell the story of the game...
So far, Costa has repaid the £32m fee that Chelsea paid to Atletico Madrid this summer, and it seems that no team can stop him in his one man assault of Premier League defences.
West Brom were effectively out of the game inside 20 minutes, as Belgian playmaker Eden Hazard made it 2-0 to Chelsea.
The Baggies switched off from a short corner, and Hazard ghosted in to the area unmarked, before driving the ball underneath the exposed Ben Foster.
And Alan Irvine's side were put to bed inside half an hour, after midfielder Claudio Yacob was sent off for a bizarre challenge on Diego Costa.
Yacob lunged in with two feet on the Chelsea striker, and unsurprisingly, referee Lee Mason brandished a straight red card for the Argentine, leaving his side out of the game with only a third of the match gone.
The star of the show was, once again, Oscar. The Brazilian has put his World Cup disaster behind him to perform excellently on a consistent basis.
Handed a new contract recently, Oscar was irresistible once again, with West Brom largely unable to pick him up as he drifted into pockets of space behind Diego Costa.
Manager Jose Mourinho watched on as his side won yet another game, and it's telling that Paddy Power have already started to pay out on bets on the Blues winning the title.
Now, the attention may even turn to whether they can go the season unbeaten, something which hasn't been done since the 2003-04 Arsenal side.