كتب : Hatem Maher
Portuguese full-back Jose Bosingwa opened the scoring in the 34th minute with a curling left-footed shot.
In-form striker Anelka doubled Chelsea's advantage four minutes later after chipping West Brom keeper Scott Carson.
The Frenchman put the result beyond doubt in the first-half's additional time with a close-range effort.
Anelka took his tally to 12 goals this season to lie on top of the scorers' chart, four clear of Wigan Athletic's Amr Zaki.
Chelsea are on top of the league table with 32 points, ahead of Liverpool on goal difference.
Earlier in the day, a Cristiano Ronaldo brace helped Manchester United hammer Stoke City 5-0 to atone for last week's 2-1 defeat to Arsenal.